# questions

tags: ['Physics', 'Semiconductors', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch0.db
title:
A d.c. battery of V volt is connected to a series combination of a resistor R and an ideal diode D as shown in the figure below. The potential difference across R will be

slug:
a-d-c-battery-of-v-volt-is-connected-to-a-series-combination-of-a-resistor-r-and-an-ideal-diode-d-a-38696

question:
<div class="question">A d.c. battery of $V$ volt is connected to a series combination of a resistor $R$ and an ideal diode $D$ as shown in the figure below. The potential difference across $R$ will be<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/afB0UvW-f7fUIb0YzgXiL2qyWTZF5Kvk43VjWQhsNW0.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 V$ when diode is forward biased</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Zero when diode is forward biased</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$V$ when diode is reverse biased</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$V$ when diode is forward biased</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Zero when diode is forward biased</span> </div>

answer:
<div class="solution">In forward biasing, the diode conducts. For ideal junction diode, the forward resistance is zero; therefore, entire applied voltage occurs across external resistance R i.e., there occurs no potential drop, so potential across $\mathrm{R}$ is $\mathrm{V}$ in forward biased.</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2016']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch0.db
title:
A deuteron of kinetic energy 50 keV is describing a circular orbit of radius 0.5 metre in a plane perpendicular to the magnetic field B . The kinetic energy of the proton that describes a circular orbit of radius 0.5 metre in the same plane with the same B is

slug:
a-deuteron-of-kinetic-energy-50-kev-is-describing-a-circular-orbit-of-radius-0-5-metre-in-a-plane-pe-87583

question:
<div class="question">A deuteron of kinetic energy $50 \mathrm{keV}$ is describing a circular orbit of radius 0.5 metre in a plane perpendicular to the magnetic field $\mathrm{B}$. The kinetic energy of the proton that describes a circular orbit of radius 0.5 metre in the same plane with the same $\mathrm{B}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$25 \mathrm{keV}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$50 \mathrm{keV}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$200 \mathrm{keV}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$100 \mathrm{keV}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$100 \mathrm{keV}$</span> </div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch0.db
title:
A die is loaded such that the probability of throwing the number \(i\) is proportional to its reciprocal. The probability that 3 appears in a single throw is-

slug:
a-die-is-loaded-such-that-the-probability-of-throwing-the-number-i-is-proportional-to-its-recipr-61344

question:
<div class="question">A die is loaded such that the probability of throwing the number \(i\) is proportional to its reciprocal. The probability that 3 appears in a single throw is-</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(3 / 22\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(3 / 11\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(9 / 22\)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None of these</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">None of these</span> </div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \mathrm{P}(\mathrm{i})=\frac{\mathrm{k}}{\mathrm{i}} \Rightarrow \mathrm{1}=\sum_{\mathrm{i}=1}^6 \mathrm{P}(\mathrm{i})=\mathrm{k} \sum_{\mathrm{i}=1}^6 \frac{1}{\mathrm{i}}=\mathrm{k} \frac{49}{20} \\<br/>&amp; \Rightarrow \mathrm{k}=\frac{20}{49} . \mathrm{P}(3)=\frac{20}{147}<br/>\end{aligned}\)</div>


title: A die is thrown 7 times. What is the probability that an even number turns up at least 4 times?
slug: a-die-is-thrown-7-times-what-is-the-probability-that-an-even-number-turns-up-at-least-4-times-28084
tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch0.db
question:
<div class="question">A die is thrown <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math> times. What is the probability that an even number turns up at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> times?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>31</mn><mn>64</mn></mfrac></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>51</mn><mn>128</mn></mfrac></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>35</mn><mn>128</mn></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></span> </div>

answer:
<div class="solution"><p>For atleast <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> times an even number, probability is</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mmultiscripts><mi>C</mi><mn>4</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>4</mn></msup><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>3</mn></msup><mo>+</mo><mmultiscripts><mi>C</mi><mn>5</mn><none></none><mprescripts></mprescripts><none></none><mn>4</mn></mmultiscripts><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>5</mn></msup><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mo>+</mo><mmultiscripts><mi>C</mi><mn>6</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>6</mn></msup><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>1</mn></msup><mo>+</mo><mmultiscripts><mi>C</mi><mn>7</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>7</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></p></div>


tags: ['Physics', 'Alternating Current', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch0.db
title:
A direct current of 5 A is superposed on an alternating current I = 10 sin Ï t flowing through the wire. The effective value of the resulting current will be

slug:
a-direct-current-of-5-a-is-superposed-on-an-alternating-current-i-10-sin-t-flowing-through-the-67526

question:
<div class="question">A direct current of $5 \mathrm{~A}$ is superposed on an alternating current $I=10 \sin \omega t$ flowing through the wire. The effective value of the resulting current will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(15 / 2) \mathrm{A}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$5 \sqrt{3} \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$5 \sqrt{5} \mathrm{~A}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$15 \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$5 \sqrt{3} \mathrm{~A}$</span> </div>

answer:
<div class="solution">Total carrent, $1=(5+10 \sin \omega \mathrm{t})$
<br/> <br/>$$
<br/> <br/>\begin{aligned}
<br/> <br/>\Rightarrow I_{\text {eff }} &amp;=\left[\frac{\int_{0}^{\mathrm{T}} \mathrm{I}^{2} \mathrm{dt}}{\int_{0}^{\mathrm{T}} \mathrm{dt}}\right]^{1 / 2} \\
<br/> <br/>&amp;=\left[\frac{1}{\mathrm{~T}} \int_{0}^{\mathrm{T}}(5+10 \sin \omega \mathrm{t})^{2} \mathrm{dt}\right]^{1 / 2} \\
<br/> <br/>&amp;=\left[\frac{1}{\mathrm{~T}} \int_{0}^{\mathrm{T}}\left(25+100 \sin \omega \mathrm{t}+100 \sin ^{2} \omega \mathrm{t}\right)\right]^{1 / 2} \\
<br/> <br/>\text { But, } \quad \frac{1}{\mathrm{~T}} \int_{0}^{\mathrm{T}} \sin \omega \mathrm{t} \mathrm{dt}=0
<br/> <br/>\end{aligned}
<br/> <br/>$$
<br/> <br/>and
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\frac{1}{\mathrm{~T}} \int_{0}^{\mathrm{T}} \sin ^{2} \omega \mathrm{t} \mathrm{dt}=\frac{1}{2} \\
<br/> <br/>\text { So, } \mathrm{I}_{\mathrm{eff}}=\left[25+\frac{1}{2} \times 100\right]^{1 / 2}=5 \sqrt{3} \mathrm{~A}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch0.db
title:
A direct current of 6 A is superimposed on an alternating current I = 10 sin Ï t flowing through a wire. The effective value of the resulting current will be

slug:
a-direct-current-of-6-a-is-superimposed-on-an-alternating-current-i-10-sin-t-flowing-through-a-52712

question:
<div class="question">A direct current of $6 \mathrm{~A}$ is superimposed on an alternating current $I=10 \sin \omega t$ flowing through a wire. The effective value of the resulting current will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$5 \sqrt{2}$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$5 \sqrt{3}$
<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"> <br/>$9.27$
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>$8.37$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$9.27$
<br/></span> </div>

answer:
<div class="solution">Given, $I=6+10 \sin \omega t$
<br/>$$
<br/>\begin{aligned}
<br/>I_{\mathrm{eft}} &amp; =\left[\frac{\left.\int_0^T I^2 d t\right]^{1 / 2}}{\int_0^T d t}=\left[\frac{1}{T} \int_0^T(6+10 \sin \omega t)^2 d t\right]^{1 / 2}\right. \\
<br/>&amp; =\left[\frac{1}{T} \int_0^T\left(36+120 \sin \omega t+100 \sin ^2 \omega t\right) d t\right]^{1 / 2}
<br/>\end{aligned}
<br/>$$
<br/>But as, $\frac{1}{T} \int_0^T \sin \omega t d t=0$ and $\frac{1}{T} \int_0^T \sin ^2 \omega t=\frac{1}{2}$
<br/>$$
<br/>\Rightarrow \quad I_{\mathrm{eff}}=\left[36+\frac{1}{2} \times 100\right]^{1 / 2}=9.27
<br/>$$
<br/>Thus, $\quad I_{\text {eff }}=9.27 \mathrm{~A}$.</div>


tags: ['Physics', 'Rotational Motion', 'JEE Main']
source_db: MarksBatch0.db
title:
A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lower most point of the disc â

slug:
a-disc-is-performing-pure-rolling-on-a-smooth-stationary-surface-with-constant-angular-velocity-as-s-26478

question:
<div class="question">A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lower most point of the disc $-$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/bfu6gxTxLm9omThWIOLYfn6k6jrae-NkE4zEXENd360.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">velocity is v, acceleration is zero</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">velocity is zero, acceleration is
<br/> <br/>zero</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">velocity is v, acceleration is $\mathrm{v}^{2} / \mathrm{R}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">velocity is zero, acceleration is $\mathrm{v}^{2} / \mathrm{R}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">velocity is zero, acceleration is $\mathrm{v}^{2} / \mathrm{R}$</span> </div>

answer:
<div class="solution">As the disc is in combined rotation and translation, each point has a tangential velocity and a linear velocity in the forward direction. From figure $\mathrm{v}_{\text {net }}$ (for lowest point) $=\mathrm{v}-\mathrm{R} \omega=\mathrm{v}-\mathrm{v}=0$
<br/> <br/>and acceleration
<br/> <br/>$=\frac{\mathrm{v}^{2}}{\mathrm{R}}+0=\frac{\mathrm{v}^{2}}{\mathrm{R}}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/EyZu6lGUGQJRjAdr1OzjBi45khqyYV8BsmqTxCDUKjw.original.fullsize.png"/><br/> <br/> <br/>(since linear speed is constant)</div>


tags: ['Physics', 'Rotational Motion', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch0.db
title:
A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lower most point of the disc â

slug:
a-disc-is-performing-pure-rolling-on-a-smooth-stationary-surface-with-constant-angular-velocity-as-s-30281

question:
<div class="question">A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lower most point of the disc $-$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/bfu6gxTxLm9omThWIOLYfn6k6jrae-NkE4zEXENd360.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">velocity is v, acceleration is zero</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">velocity is zero, acceleration is
<br/> <br/>zero</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">velocity is v, acceleration is $\mathrm{v}^{2} / \mathrm{R}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">velocity is zero, acceleration is $\mathrm{v}^{2} / \mathrm{R}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">velocity is zero, acceleration is $\mathrm{v}^{2} / \mathrm{R}$</span> </div>

answer:
<div class="solution">As the disc is in combined rotation and translation, each point has a tangential velocity and a linear velocity in the forward direction. From figure $\mathrm{v}_{\text {net }}$ (for lowest point) $=\mathrm{v}-\mathrm{R} \omega=\mathrm{v}-\mathrm{v}=0$
<br/> <br/>and acceleration
<br/> <br/>$=\frac{\mathrm{v}^{2}}{\mathrm{R}}+0=\frac{\mathrm{v}^{2}}{\mathrm{R}}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/EyZu6lGUGQJRjAdr1OzjBi45khqyYV8BsmqTxCDUKjw.original.fullsize.png"/><br/> <br/> <br/>(since linear speed is constant)</div>


slug: a-disc-is-rolling-without-slipping-on-a-surface-the-radius-of-the-disc-is-r-at-t-0-the-top-mo-52161
tags: ['Physics', 'Rotational Motion', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch0.db
title:
A disc is rolling without slipping on a surface. The radius of the disc is R . At t = 0 , the top most point on the disc is A as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is

question:
<div class="question">A disc is rolling without slipping on a surface. The radius of the disc is $R$. At $t=0$, the top most point on the disc is $\mathrm{A}$ as shown in figure. When the disc completes half of its rotation, the displacement of point $A$ from its initial position is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/q-SlnnL2YNKWPjSCnEgbYs-9BTAVQuKIBpDRx5eQUoE.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{R} \sqrt{\left(\pi^2+4\right)}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{R} \sqrt{\left(\pi^2+1\right)}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 \mathrm{R}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \mathrm{R} \sqrt{\left(1+4 \pi^2\right)}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{R} \sqrt{\left(\pi^2+4\right)}$</span> </div>

answer:
<div class="solution">(a) From figure,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Djr7jOTnwC9j_KyyquLbu_JqUqhoVr-OQSeyH17AjIk.original.fullsize.png"/><br/><br/>Displacement,<br/>$\mathrm{BA}=\sqrt{(2 \mathrm{R})^2+(\pi \mathrm{R})^2}=\mathrm{R} \sqrt{4+\pi^2}$</div>


slug: a-flask-contains-hydrogen-and-oxygen-in-the-ratio-of-2-1-by-mass-at-temperature-2-7-c-the-ra-61565
tags: ['Physics', 'Kinetic Theory of Gases', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch0.db
title:
A flask contains hydrogen and oxygen in the ratio of 2 : 1 by mass at temperature 2 7 â C . The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :

question:
<div class="question">A flask contains hydrogen and oxygen in the ratio of $2: 1$ by mass at temperature $27^{\circ} \mathrm{C}$. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>2 : 1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>1 : 1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>1 : 4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>4 : 1</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>1 : 1</span> </div>

answer:
<div class="solution">Average kinetic energy for diatomic gases<br/>$\begin{aligned}<br/>&amp; \mathrm{K}_{\mathrm{av}}=\frac{5}{2} \mathrm{kT} \\<br/>&amp; \therefore \frac{\left(\mathrm{K}_{\mathrm{av}}\right)_{\mathrm{H}}}{\left(\mathrm{K}_{\mathrm{av}}\right)_{\mathrm{O}}}=\frac{(27+273)}{(27+273)}=1<br/>\end{aligned}$</div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch0.db
title:
A frictionless wire AB is fixed on a sphere of radius R . A very small spherical ball slips on this wire. The time taken by this ball to slip from A to B is

slug:
a-frictionless-wire-ab-is-fixed-on-a-sphere-of-radius-r-a-very-small-spherical-ball-slips-on-this-47071

question:
<div class="question">A frictionless wire $\mathrm{AB}$ is fixed on a sphere of radius $\mathrm{R}$. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to $\mathrm{B}$ is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/r_OrMPvilqMNy6lx1g52JXylmmTCE4Iq5qfXm1-nk1k.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\sqrt{2 g R}}{g \cos \theta}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \sqrt{g R} \cdot \frac{\cos \theta}{g}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$2 \sqrt{\frac{R}{g}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{g R}{\sqrt{g \cos \theta}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \sqrt{\frac{R}{g}}$</span> </div>

answer:
<div class="solution">Acceleration of body along $\mathrm{AB}$ is g $\cos \theta$ Distance travelled in time $\mathrm{t}$ sec $=$
<br/> <br/>$A B=\frac{1}{2}(g \cos \theta) t^{2}$
<br/> <br/>From $\Delta \mathrm{ABC}, \mathrm{AB}=2 \mathrm{R} \cos \theta$
<br/> <br/>Thus, $2 \mathrm{R} \cos \theta=\frac{1}{2} g \cos \theta t^{2}$
<br/> <br/>$\Rightarrow t^{2}=\frac{4 R}{g} \Rightarrow t=2 \sqrt{\frac{R}{g}}$</div>


slug: a-gas-has-molar-heat-capacity-c-37-55-j-mol-1-k-1-in-this-process-p-t-constant-the-numb-72938
tags: ['Physics', 'Kinetic Theory of Gases', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch0.db
title:
A gas has molar heat capacity C = 37 . 55 J mol - 1 K - 1 , in this process p T = constant. The number of degree of freedom of the molecule of gas is

question:
<div class="question">A gas has molar heat capacity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>37</mn><mo>.</mo><mn>55</mn><mo> </mo><mi mathvariant="normal">J</mi><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">K</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, in this process <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>T</mi><mo>=</mo></math> constant. The number of degree of freedom of the molecule of gas is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></span> </div>

answer:
<div class="solution"><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>37</mn><mo>.</mo><mn>55</mn><mo> </mo><mi mathvariant="normal">J</mi><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">K</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p>Also, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>T</mi><mo>=</mo></math> constant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></p><p>According to ideal gas equation, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mi>R</mi><mi>T</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mo> </mo><mo> </mo><mi>p</mi><mo>=</mo><mfrac><mrow><mi>R</mi><mi>T</mi></mrow><mi>V</mi></mfrac><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi mathvariant="normal">i</mi></mfenced></math></p><p>Putting the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> in Eq. (i), we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>R</mi><mi>T</mi></mrow><mi>V</mi></mfrac><mo>×</mo><mi>T</mi><mo>=</mo><mi>K</mi><mo> </mo><mo> </mo><mo> </mo><mo>⇒</mo><mo> </mo><mo> </mo><mo> </mo><mi>V</mi><mo>=</mo><mfrac><mrow><mi>R</mi><msup><mi>T</mi><mn>2</mn></msup></mrow><mi>K</mi></mfrac><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi>ii</mi></mfenced></math></p><p>On differentiating above equation both sides, we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>d</mi><mi>V</mi></mrow><mrow><mi>d</mi><mi>T</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mi>R</mi><mi>T</mi></mrow><mi>K</mi></mfrac><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi>iii</mi></mfenced></math><br/>But <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>T</mi><mi>K</mi></mfrac><mo>=</mo><mfrac><mn>1</mn><mi>p</mi></mfrac><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced close="]" open="["><mrow><mi>from</mi><mi>Eq</mi><mo>.</mo><mo> </mo><mo> </mo><mfenced><mi mathvariant="normal">i</mi></mfenced></mrow></mfenced></math><br/>Hence, Eq. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>iii</mi></mfenced></math>becomes</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>d</mi><mi>V</mi></mrow><mrow><mi>d</mi><mi>T</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mo> </mo><mi mathvariant="normal">R</mi></mrow><mi>p</mi></mfrac></math><br/>So, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><msub><mi>C</mi><mi>V</mi></msub><mo>+</mo><mfrac><mrow><mi>p</mi><mi>d</mi><mi>V</mi></mrow><mrow><mi>d</mi><mi>T</mi></mrow></mfrac></math><br/>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><msub><mi>C</mi><mi>V</mi></msub><mo>+</mo><mfrac><mrow><mi>p</mi><mo>×</mo><mn>2</mn><mo> </mo><mi mathvariant="normal">R</mi></mrow><mi>p</mi></mfrac><mo>=</mo><msub><mi>C</mi><mi>V</mi></msub><mo>+</mo><mn>2</mn><mo> </mo><mi mathvariant="normal">R</mi></math><br/>or <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mi>V</mi></msub><mo>=</mo><mi>C</mi><mo>-</mo><mn>2</mn><mo> </mo><mi mathvariant="normal">R</mi><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi>iv</mi></mfenced></math></p><p>As <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mi>V</mi></msub><mo>=</mo><mfrac><mrow><mi>n</mi><mi>R</mi></mrow><mn>2</mn></mfrac><mo>,</mo></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo></math> number of degrees of freedom.<br/>Putting the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mi>V</mi></msub></math> in Eq. (iv), we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mi>R</mi></mrow><mn>2</mn></mfrac><mo>=</mo><mi>C</mi><mo>-</mo><mn>2</mn><mo> </mo><mi mathvariant="normal">R</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo> </mo><mfenced><mrow><mi>C</mi><mo>-</mo><mn>2</mn><mo> </mo><mi mathvariant="normal">R</mi></mrow></mfenced></mrow><mi>R</mi></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mo> </mo><mfenced><mrow><mn>37</mn><mo>.</mo><mn>55</mn><mo>-</mo><mn>2</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mn>8</mn><mo>.</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mn>5</mn><mo>.</mo><mn>048</mn><mo>≈</mo><mn>5</mn></math></p></div>


slug: a-gas-x-at-1-atm-is-bubbled-through-a-solution-containing-a-mixture-of-1-m-y-and-1-m-z-at-2-92846
tags: ['Chemistry', 'Redox Reactions', 'BITSAT', 'BITSAT 2011']
answer: <div class="solution">The more the reduction potential, the more the oxidising power.</div>
source_db: MarksBatch0.db
title:
A gas X at 1 atm is bubbled through a solution containing a mixture of 1 M Y â and 1 M Z â at 2 5 â C . If the reduction potential is Z > Y > X , then

question:
<div class="question">A gas $X$ at 1 atm is bubbled through a solution containing a mixture of $1 \mathrm{M} \mathrm{Y}^{-}$ and $1 \mathrm{M} \mathrm{Z}^{-}$ at $25^{\circ} \mathrm{C}$. If the reduction potential is $Z&gt;Y&gt;X$, then</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{Y}$ will oxidise $\mathrm{X}$ and $\mathrm{not} \mathrm{Z}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Y}$ will oxidise $Z$ and $\mathrm{not} \mathrm{X}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Y}$ will oxidise both $\mathrm{X}$ and $\mathrm{Z}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Y}$ will reduce both $\mathrm{X}$ and $\mathrm{Z}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Y}$ will oxidise $\mathrm{X}$ and $\mathrm{not} \mathrm{Z}$</span> </div>


slug: a-gaseous-reaction-x-2-g-y-2-1-z-g-there-is-increase-in-pressure-from-100-mm-t-46676
tags: ['Chemistry', 'Chemical Kinetics', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch0.db
title:
A gaseous reaction X 2 â ( g ) â¶ Y + 2 1 â Z ( g ) There is increase in pressure from 100 mm to 120 mm in 5 minutes. The rate of disappearance of X 2 â is

question:
<div class="question">A gaseous reaction $\mathrm{X}_{2}(\mathrm{~g}) \longrightarrow \mathrm{Y}+\frac{1}{2} \mathrm{Z}(\mathrm{g})$
<br/> <br/>There is increase in pressure from $100 \mathrm{~mm}$ to 120 $\mathrm{mm}$ in 5 minutes. The rate of disappearance of $\mathrm{X}_{2}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$8 \mathrm{~mm} \mathrm{~min}^{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \mathrm{~mm} \mathrm{~min}^{-1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$16 \mathrm{~mm} \mathrm{~min}^{-1}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4 \mathrm{~mm} \min ^{-1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$8 \mathrm{~mm} \mathrm{~min}^{-1}$</span> </div>

answer:
<div class="solution">The increase in pressure shows the increase in conc. of $Z$. Rate of appearance of $Z=$
<br/> <br/>$$
<br/> <br/>\frac{120-100}{5}=4 \mathrm{~mm} \mathrm{~min}^{-1}
<br/> <br/>$$
<br/> <br/>Rate of disappearance of $\mathrm{X}_{2}=2 \times$ rate of appearance of $Z$ $=2 \times 4 \mathrm{~mm} \mathrm{~min}^{-1}=8 \mathrm{~mm} \mathrm{~min}^{-1}$</div>


tags: ['Physics', 'Gravitation', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch0.db
title:
A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km . Then, the time period of a sky satellite orbiting a few 100 km above the earth's surface R = 64000 km will approximately be

slug:
a-geostationary-satellite-orbits-around-the-earth-in-a-circular-orbit-of-radius-36000-km-then-the-46476

question:
<div class="question">A geostationary satellite orbits around the earth in a circular orbit of radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36000</mn><mo> </mo><mi>km</mi></math>. Then, the time period of a sky satellite orbiting a few <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mi>km</mi></math> above the earth's surface <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>R</mi><mo>=</mo><mn>64000</mn><mo> </mo><mi>km</mi></mrow></mfenced></math> will approximately be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo> </mo><mi mathvariant="normal">h</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">h</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi mathvariant="normal">h</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi mathvariant="normal">h</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi mathvariant="normal">h</mi></math></span> </div>

answer:
<div class="solution"><p>By Kepler's law of planetary motion,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>T</mi><mn>2</mn></msup><mo>∝</mo><msup><mi>r</mi><mn>3</mn></msup></math>, hence <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>T</mi><mn>1</mn><mn>2</mn></msubsup><mo>∝</mo><msubsup><mi>r</mi><mn>1</mn><mn>3</mn></msubsup></math></p><p>Similarly <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>T</mi><mn>2</mn><mn>2</mn></msubsup><mo>∝</mo><msubsup><mi>r</mi><mn>2</mn><mn>3</mn></msubsup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><msubsup><mi>T</mi><mn>1</mn><mn>2</mn></msubsup><mo>∝</mo><msup><mfenced><mn>36000</mn></mfenced><mn>3</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>T</mi><mn>2</mn><mn>2</mn></msubsup><mo>∝</mo><msup><mfenced><mrow><mn>6400</mn><mo>+</mo><mi>h</mi></mrow></mfenced><mn>3</mn></msup></math></p><p>Therefore, </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><msub><mi>T</mi><mn>2</mn></msub></mfenced><mn>2</mn></msup><mo>=</mo><msubsup><mi>T</mi><mn>1</mn><mn>2</mn></msubsup><msup><mfenced><mfrac><mrow><mn>6400</mn><mo>+</mo><mi>h</mi></mrow><mn>36000</mn></mfrac></mfenced><mn>3</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&gt;</mo><msubsup><mi>T</mi><mn>1</mn><mn>2</mn></msubsup><msup><mfenced close="]" open="["><mfrac><mn>6400</mn><mn>3600</mn></mfrac></mfenced><mn>3</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&gt;</mo><msup><mfenced><mn>24</mn></mfenced><mn>2</mn></msup><msup><mfenced close="]" open="["><mfrac><mn>8</mn><mn>45</mn></mfrac></mfenced><mn>3</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><msub><mi>T</mi><mn>2</mn></msub><mo>&gt;</mo><mfrac><mrow><mn>24</mn><mo>×</mo><mn>8</mn><mo>×</mo><msqrt><mn>8</mn></msqrt></mrow><mrow><mn>45</mn><mo>×</mo><msqrt><mn>45</mn></msqrt></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&gt;</mo><mn>1</mn><mo>.</mo><mn>8</mn><mo> </mo><mi mathvariant="normal">h</mi></math></p><p>So, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mn>2</mn></msub><mo>≅</mo><mn>2</mn><mo> </mo><mi mathvariant="normal">h</mi></math></p></div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch0.db
title:
A glass capillary tube of internal radius r = 0.25 mm is immersed in water. The top end of the tube projected by 2 cm above the surface of the water. At what angle does the liquid meet the tube? Surface tension of water = 0.7 N / m

slug:
a-glass-capillary-tube-of-internal-radius-r-0-25-mm-is-immersed-in-water-the-top-end-of-the-tube-46180

question:
<div class="question">A glass capillary tube of internal radius $\mathrm{r}=0.25$ $\mathrm{mm}$ is immersed in water. The top end of the tube projected by $2 \mathrm{~cm}$ above the surface of the water. At what angle does the liquid meet the tube? Surface tension of water $=0.7 \mathrm{~N} / \mathrm{m}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\theta=90^{\circ}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\quad \theta=70^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\theta=45^{\circ}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\theta=35^{\circ}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad \theta=70^{\circ}$</span> </div>

answer:
<div class="solution">Water wets glass and so the angle of contact is zero. For full rise, neglecting the small mass in the meniscus
<br/> <br/>$$
<br/> <br/>\begin{aligned}
<br/> <br/>2 \pi \mathrm{T} &amp;=\pi \mathrm{r}^{2} \mathrm{~h} \rho \mathrm{g} \Rightarrow \mathrm{h}=\frac{2 \mathrm{~T}}{\mathrm{r} \rho \mathrm{g}}\left[\because \text { water wets glass, } \theta=0^{\circ}\right] \\
<br/> <br/>&amp;=\frac{2 \times 007}{0.25 \times 10^{-3} \times 1000 \times 9.8}
<br/> <br/>\end{aligned}
<br/> <br/>$$
<br/> <br/>As the tube is only $2 \mathrm{~cm}$ above the water and so, water will rise by $2 \mathrm{~cm}$ and meet the tube at an angle such that,
<br/> <br/>$$
<br/> <br/>\begin{aligned}
<br/> <br/>2 \pi r &amp; \operatorname{T} \cos \theta=\pi r^{2} h^{\prime} \rho g \\
<br/> <br/>\Rightarrow &amp; 2 T \cos \theta=h^{\prime} r \rho g \\
<br/> <br/>\Rightarrow \cos \theta &amp;=\frac{h^{\prime} r \rho g}{2 T} \\
<br/> <br/>&amp;=\frac{2 \times 10^{-2} \times 0.25 \times 10^{-3} \times 1000 \times 9.8}{2 \times 0.07}
<br/> <br/>\end{aligned}
<br/> <br/>$$
<br/> <br/>The liquid will meet the tube at an angle, $\theta$ $\cong 70^{\circ}$</div>


tags: ['Chemistry', 'Chemical Kinetics', 'JEE Main']
source_db: MarksBatch0.db
title:
A graph is plotted between log K versus 1 T for calculation of activation energy E a . The correct plot is

slug:
a-graph-is-plotted-between-log-k-versus-1-t-for-calculation-of-activation-energy-e-a-the-correct-p-19121

question:
<div class="question"><p>A graph is plotted between log <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">K</mi></math> versus <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi mathvariant="normal">T</mi></mfrac></math> for calculation of activation energy <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub></mfenced></math>. The correct plot is</p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/95bf569a-d489-4f23-879f-7c451762bb6a-image.png" style="width: 200px; height: 180px;"/></p></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/dc277033-e689-451f-957f-db816643eb9f-image.png" style="width: 200px; height: 185px;"/></p></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/c8fcacc6-93ca-4780-839b-b5d0c06302c5-image.png" style="width: 200px; height: 186px;"/></p></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ac619cb0-46a5-4bbf-b5af-c408f8e2774f-image.png" style="width: 200px; height: 161px;"/></p></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/dc277033-e689-451f-957f-db816643eb9f-image.png" style="width: 200px; height: 185px;"/></p></span> </div>

answer:
<div class="solution"><p>According to Arrhenius equation,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">k</mi><mo>∝</mo><mi mathvariant="normal">T</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">k</mi><mo>=</mo><msup><mi>Ae</mi><mrow><mo>−</mo><mi>Ea</mi><mo>​</mo><mo>/</mo><mi>RT</mi></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>logk</mi><mo>=</mo><mi>logA</mi><mo>-</mo><mfrac><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub><mrow><mn>2</mn><mo>.</mo><mn>303</mn><mo>×</mo><mi mathvariant="normal">R</mi></mrow></mfrac><mo>​</mo><mo>​</mo><mo>×</mo><mfrac><mn>1</mn><mi mathvariant="normal">T</mi></mfrac><mo>​</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>=</mo><mi>mx</mi><mo>+</mo><mi mathvariant="normal">c</mi></math>, the equation of straight line</p><p>The value of log <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">k</mi></math> should increase uniformily with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">T</mi></math> or decrease with <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi mathvariant="normal">T</mi></mfrac></math>.</p><p>               <img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/dc277033-e689-451f-957f-db816643eb9f-image.png" style="width: 200px; height: 185px;"/></p><p>From this, that the slope is negative, which means that angle with x - axis is greater than 90° also that the point on which the straight line of graph intercepts the y - axis is log A which is positive.</p><p>Hence all the conclusions point out towards option b as it has negative slope and a positive y intercept.</p></div>


tags: ['Chemistry', 'Chemical Kinetics', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch0.db
title:
A graph is plotted between log K versus 1 T for calculation of activation energy E a . The correct plot is

slug:
a-graph-is-plotted-between-log-k-versus-1-t-for-calculation-of-activation-energy-e-a-the-correct-p-81572

question:
<div class="question"><p>A graph is plotted between log <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">K</mi></math> versus <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi mathvariant="normal">T</mi></mfrac></math> for calculation of activation energy <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub></mfenced></math>. The correct plot is</p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/95bf569a-d489-4f23-879f-7c451762bb6a-image.png" style="width: 200px; height: 180px;"/></p></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/dc277033-e689-451f-957f-db816643eb9f-image.png" style="width: 200px; height: 185px;"/></p></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/c8fcacc6-93ca-4780-839b-b5d0c06302c5-image.png" style="width: 200px; height: 186px;"/></p></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ac619cb0-46a5-4bbf-b5af-c408f8e2774f-image.png" style="width: 200px; height: 161px;"/></p></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/dc277033-e689-451f-957f-db816643eb9f-image.png" style="width: 200px; height: 185px;"/></p></span> </div>

answer:
<div class="solution"><p>According to Arrhenius equation,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">k</mi><mo>∝</mo><mi mathvariant="normal">T</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">k</mi><mo>=</mo><msup><mi>Ae</mi><mrow><mo>−</mo><mi>Ea</mi><mo>​</mo><mo>/</mo><mi>RT</mi></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>logk</mi><mo>=</mo><mi>logA</mi><mo>-</mo><mfrac><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub><mrow><mn>2</mn><mo>.</mo><mn>303</mn><mo>×</mo><mi mathvariant="normal">R</mi></mrow></mfrac><mo>​</mo><mo>​</mo><mo>×</mo><mfrac><mn>1</mn><mi mathvariant="normal">T</mi></mfrac><mo>​</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>=</mo><mi>mx</mi><mo>+</mo><mi mathvariant="normal">c</mi></math>, the equation of straight line</p><p>The value of log <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">k</mi></math> should increase uniformily with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">T</mi></math> or decrease with <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi mathvariant="normal">T</mi></mfrac></math>.</p><p>               <img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/dc277033-e689-451f-957f-db816643eb9f-image.png" style="width: 200px; height: 185px;"/></p><p>From this, that the slope is negative, which means that angle with x - axis is greater than 90° also that the point on which the straight line of graph intercepts the y - axis is log A which is positive.</p><p>Hence all the conclusions point out towards option b as it has negative slope and a positive y intercept.</p></div>


slug: a-gun-fires-two-bullets-at-6-0-and-3-0-with-horizontal-the-bullets-strike-at-some-horizonta-66883
tags: ['Physics', 'Motion In Two Dimensions', 'BITSAT', 'BITSAT 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$3: 1$</span> </div>
source_db: MarksBatch0.db
title:
A gun fires two bullets at 6 0 â and 3 0 â with horizontal. The bullets strike at some horizontal distance. The ratio of maximum height for the two bullets is in the ratio of

question:
<div class="question">A gun fires two bullets at $60^{\circ}$ and $30^{\circ}$ with horizontal. The bullets strike at some horizontal distance. The ratio of maximum height for the two bullets is in the ratio of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2: 1$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$3: 1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4: 1$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1: 1$</span> </li> </ul>

answer:
<div class="solution">The bullets are fired at the same initial speed
<br/> <br/>$\begin{array}{l}
<br/> <br/>\frac{\mathrm{H}}{\mathrm{H}^{\prime}}=\frac{\mathrm{u}^{2} \sin ^{2} 60^{\circ}}{2 \mathrm{~g}} \times \frac{2 \mathrm{~g}}{\mathrm{u}^{2} \sin ^{2} 30^{\circ}}=\frac{\sin ^{2} 60^{\circ}}{\sin ^{2} 30^{\circ}} \\
<br/> <br/>=\frac{(\sqrt{3} / 2)^{2}}{(1 / 2)^{2}}=\frac{3}{1}
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch0.db
title:
A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V . The potential at a distance of 2 cm from the centre of the sphere is

slug:
a-hollow-metal-sphere-of-radius-5-cm-is-charged-such-that-the-potential-on-its-surface-is-10-v-the-52395

question:
<div class="question">A hollow metal sphere of radius $5 \mathrm{~cm}$ is charged such that the potential on its surface is $10 \mathrm{~V}$. The potential at a distance of $2 \mathrm{~cm}$ from the centre of the sphere is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">zero</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$10 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10 / 3 \mathrm{~V}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10 \mathrm{~V}$</span> </div>

answer:
<div class="solution">Potential at any point inside the sphere $=$ potential at the surface of the sphere $=10 \mathrm{~V}$.</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch0.db
title:
A horizontal overhead powerline is at height of 4 m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is ( Î¼ 0 â = 4 Ï Ã 1 0 â 7 Tm A â 1 )

slug:
a-horizontal-overhead-powerline-is-at-height-of-4-m-from-the-ground-and-carries-a-current-of-100-a-f-46110

question:
<div class="question">A horizontal overhead powerline is at height of $4 \mathrm{~m}$ from the ground and carries a current of $100 \mathrm{~A}$ from east to west. The magnetic field directly below it on the ground is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}\right)$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2.5 \times 10^{-7} \mathrm{~T}$ southward</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5 \times 10^{-6}$ T northward</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$5 \times 10^{-6} \mathrm{~T}$ southward</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2.5 \times 10^{-7}$ T northward</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$5 \times 10^{-6} \mathrm{~T}$ southward</span> </div>

answer:
<div class="solution">The magnetic field is
<br/>$\mathrm{B}=\frac{\mu_{0}}{4 \pi} \frac{2 \mathrm{I}}{\mathrm{r}}=10^{-7} \times \frac{2 \times 100}{4}=5 \times 10^{-6} \mathrm{~T}$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/fXNqXasjtRkq7PU3M79o92MfBcmfgd2vd8nB1h7sNF4.original.fullsize.png"/><br/> <br/>According to right hand palm rule, the magnetic field is directed towards south.</div>


tags: ['Mathematics', 'Heights and Distances', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch0.db
title:
A house subtends a right angle at the window of a opposite house and the angle of elevation of the window from the bottom of the first house is 60 . If the distance between two houses be 6 m , then the height of the first house is

slug:
a-house-subtends-a-right-angle-at-the-window-of-a-opposite-house-and-the-angle-of-elevation-of-the-w-86835

question:
<div class="question">A house subtends a right angle at the window of a opposite house and the angle of elevation of the window from the bottom of the first house is $60$. If the distance between two houses be $6 \mathrm{~m}$, then the height of the first house is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"> <br/>$8 \sqrt{3} \mathrm{~m}$
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$6 \sqrt{3} \mathrm{~m}$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$4 \sqrt{3} \mathrm{~m}$
<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$8 \sqrt{3} \mathrm{~m}$
<br/></span> </div>

answer:
<div class="solution">Let $P Q$ be the house subtending a right angle at the window $B$ of opposite house $A B$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/0V7dsPYHXJPSlfmOThYsY38RGsVYM4qnm7QqqLpWp0s.original.fullsize.png"/><br/> <br/>In $\triangle P A B$, we have 
<br/>$\tan 60^{\circ}=\frac{A B}{6}=A B=6 \sqrt{3} \mathrm{~m}$
<br/>In $\triangle C B Q$, we have
<br/>$\tan 30^{\circ}=\frac{h-C P}{B C}$
<br/>$\begin{array}{ll}\Rightarrow &amp; \frac{1}{\sqrt{3}}=\frac{h-6 \sqrt{3}}{6} \quad[\because A B=C P, B C=A P] \\ \Rightarrow &amp; h=6\left(\sqrt{3}+\frac{1}{\sqrt{3}}\right) \\ \Rightarrow &amp; h=8 \sqrt{3} \mathrm{~m}\end{array}$</div>


tags: ['Physics', 'Thermodynamics', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch0.db
title:
A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is 81 16 â . Then the ratio of C V â C P â â will be.

slug:
a-hypothetical-gas-expands-adiabatically-such-that-its-volume-changes-from-08-litres-to-27-litres-i-32795

question:
<div class="question">A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{81}$. Then the ratio of $\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}$ will be.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{4}{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3}{1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{3}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{4}{3}$</span> </div>

answer:
<div class="solution">In adiabatic process<br/>$\begin{aligned}<br/>&amp; \mathrm{PV}^\gamma=\text { constant } \\<br/>&amp; \Rightarrow \quad \mathrm{P}_1 \mathrm{~V}_1^\gamma=\mathrm{P}_2 \mathrm{~V}_2^\gamma \\<br/>&amp; \Rightarrow \quad \frac{\mathrm{P}_1}{\mathrm{P}_2}=\left(\frac{\mathrm{V}_2}{\mathrm{~V}_1}\right)^\gamma \Rightarrow \frac{81}{16}=\left(\frac{27}{8}\right)^\gamma \\<br/>&amp; \Rightarrow\left(\frac{9}{4}\right)^2=\left(\frac{9 \times 3}{4 \times 2}\right)^\gamma \Rightarrow\left(\frac{9}{4}\right)^{2-\gamma}=\left(\frac{3}{2}\right)^\gamma \\<br/>&amp; \Rightarrow\left(\frac{9}{4}\right)^{2-\gamma}=\left(\frac{9}{4}\right)^{\gamma / 2} \Rightarrow 2-\gamma=\frac{\gamma}{2} \\<br/>&amp; \Rightarrow 2=\frac{3}{2} \gamma \Rightarrow \gamma=\frac{4}{3}<br/>\end{aligned}$</div>


tags: ['Chemistry', 'Hydrocarbons', 'JEE Main']
source_db: MarksBatch0.db
title:
A is an optically inactive alkyl chloride which on reaction with aqueous KOH gives B . B on heating with Cu at 30 0 â C gives an alkene C , what are A and C

slug:
a-is-an-optically-inactive-alkyl-chloride-which-on-reaction-with-aqueous-koh-gives-b-b-on-heating-91899

question:
<div class="question">A is an optically inactive alkyl chloride which on reaction with aqueous $\mathrm{KOH}$ gives $\mathrm{B}$. $\mathrm{B}$ on heating with $\mathrm{Cu}$ at $300^{\circ} \mathrm{C}$ gives an alkene $\mathrm{C}$, what are $\mathrm{A}$ and $\mathrm{C}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}, \mathrm{CH}_{2}=\mathrm{CH}_{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Me}_{3} \mathrm{CCl}, \mathrm{MeCH}=\mathrm{CH} \cdot \mathrm{Me}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{Me}_{3} \mathrm{CCl}, \mathrm{Me}_{2} \mathrm{C}=\mathrm{CH}_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Me}_{2} \mathrm{CH} . \mathrm{CH}_{2} \mathrm{Cl} \mathrm{Me}_{2} \mathrm{C}=\mathrm{CH}_{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Me}_{3} \mathrm{CCl}, \mathrm{Me}_{2} \mathrm{C}=\mathrm{CH}_{2}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/r_jzUIv-Nw7CGGxbT1JMECZ_8-bXs_RLrzK7s_1eGWM.original.fullsize.png"/><br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/A1h6mVXZ-ohdv4SfRu_QUNMXYUlgXa4q03B3lnVhDZI.original.fullsize.png"/><br/><br/>OR<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/aOvKvW1brEWLAWQwhcMdHf0OfbXvuvTVQE1gw4h2F5Y.original.fullsize.png"/></div>


tags: ['Chemistry', 'Hydrocarbons', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch0.db
title:
A is an optically inactive alkyl chloride which on reaction with aqueous KOH gives B . B on heating with Cu at 30 0 â C gives an alkene C , what are A and C

slug:
a-is-an-optically-inactive-alkyl-chloride-which-on-reaction-with-aqueous-koh-gives-b-b-on-heating-41354

question:
<div class="question">A is an optically inactive alkyl chloride which on reaction with aqueous $\mathrm{KOH}$ gives $\mathrm{B}$. $\mathrm{B}$ on heating with $\mathrm{Cu}$ at $300^{\circ} \mathrm{C}$ gives an alkene $\mathrm{C}$, what are $\mathrm{A}$ and $\mathrm{C}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}, \mathrm{CH}_{2}=\mathrm{CH}_{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Me}_{3} \mathrm{CCl}, \mathrm{MeCH}=\mathrm{CH} \cdot \mathrm{Me}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{Me}_{3} \mathrm{CCl}, \mathrm{Me}_{2} \mathrm{C}=\mathrm{CH}_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Me}_{2} \mathrm{CH} . \mathrm{CH}_{2} \mathrm{Cl} \mathrm{Me}_{2} \mathrm{C}=\mathrm{CH}_{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Me}_{3} \mathrm{CCl}, \mathrm{Me}_{2} \mathrm{C}=\mathrm{CH}_{2}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/r_jzUIv-Nw7CGGxbT1JMECZ_8-bXs_RLrzK7s_1eGWM.original.fullsize.png"/><br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/A1h6mVXZ-ohdv4SfRu_QUNMXYUlgXa4q03B3lnVhDZI.original.fullsize.png"/><br/><br/>OR<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/aOvKvW1brEWLAWQwhcMdHf0OfbXvuvTVQE1gw4h2F5Y.original.fullsize.png"/></div>


tags: ['Mathematics', 'Heights and Distances', 'BITSAT', 'BITSAT 2011']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">12</span> </div>
answer: <div class="solution">Length of ladder \(=\frac{6 \sqrt{3}}{\sin 60^{\circ}}=12 \mathrm{~m}\)</div>
source_db: MarksBatch0.db
title:
A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of \(60^{\circ}\) with the horizontal and height of the house be \(6 \sqrt{3}\) meters, then the length of the ladder in meters is

slug:
a-ladder-rests-against-a-wall-so-that-its-top-touches-the-roof-of-the-house-if-the-ladder-makes-an-39841

question:
<div class="question">A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of \(60^{\circ}\) with the horizontal and height of the house be \(6 \sqrt{3}\) meters, then the length of the ladder in meters is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(12 \sqrt{3}\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">12</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(12 / \sqrt{3}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>


slug: a-large-drop-of-oil-density-0-8-g-cm-3-and-viscosity-0-floats-up-through-a-column-of-ano-55107
tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch0.db
title:
A large drop of oil (density 0.8 g / cm 3 and viscosity Î· 0 â ) floats up through a column of another liquid (density 1.2 g / cm 3 and viscosity Î· L â ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on:

question:
<div class="question">A large drop of oil (density $0.8 \mathrm{~g} / \mathrm{cm}^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2 \mathrm{~g} / \mathrm{cm}^{3}$ and viscosity $\eta_{\mathrm{L}}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\eta_{0}$ only</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\eta_{L}$ only</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">both on $\eta_{0}$ and $\eta_{\mathrm{L}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">neither $\eta_{0}$ nor $\eta_{L}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\eta_{L}$ only</span> </div>

answer:
<div class="solution">Forces of viscosity arise in a fluid when different sections of the fluid move with different velocities. Here, there is no such motion inside the oil drop and hence the viscosity of oil does not come into play.</div>


tags: ['Physics', 'Ray Optics', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch0.db
title:
A lens having focal length f and aperture of diameter d forms an image of intensity I . Aperture of diameter 2 d â in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively:

slug:
a-lens-having-focal-length-f-and-aperture-of-diameter-d-forms-an-image-of-intensity-i-aperture-of-79639

question:
<div class="question">A lens having focal length $f$ and aperture of diameter $d$ forms an image of intensity $I$. Aperture of diameter $\frac{d}{2}$ in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$f$ and $\frac{I}{4}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3 f}{4}$ and $\frac{I}{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$f$ and $\frac{3 I}{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{f}{2}$ and $\frac{I}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$f$ and $\frac{3 I}{4}$</span> </div>

answer:
<div class="solution">Bycovering aperture, focal length does not change. But intensity is reduced by $\frac{1}{4}$ times
<br/> <br/>as aperture diameter $\frac{d}{2}$ is covered.
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\therefore \quad I^{\prime}=I-\frac{I}{4}=\frac{3 I}{4} \\
<br/> <br/>\therefore \quad \text { New focal length }=\mathrm{f} \text { and intensity }=\frac{3 I}{4} .
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Physics', 'Current Electricity', 'JEE Main']
source_db: MarksBatch0.db
title:
A letter'A' is constructed of a uniform wire with resistance 1.0Î© per cm , The sides of the letter are 20 cm and the cross piece in the middle is 10 cm long. The apex angle is 60. The resistance between the ends of the legs is close to:

slug:
a-letter-a-is-constructed-of-a-uniform-wire-with-resistance-1-0-per-cm-the-sides-of-the-letter-90166

question:
<div class="question">A letter'A' is constructed of a uniform wire with resistance $1.0 \Omega$ per $\mathrm{cm}$, The sides of the letter are $20 \mathrm{~cm}$ and the cross piece in the middle is 10 $\mathrm{cm}$ long. The apex angle is $60 .$ The resistance between the ends of the legs is close to:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$50.0 \Omega$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 \Omega$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$36.7 \Omega$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$26.7 \Omega$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$26.7 \Omega$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Y5sbUODQvszObE9Pnn_44LN51U94r0ntiNbllSp34b8.original.fullsize.png"/><br/> <br/>For ADE $\frac{1}{R^{\prime}}=\frac{1}{2 x}+\frac{1}{10} \quad$ or $\quad R^{\prime}=\frac{20 x}{10+2 x}$
<br/>$\mathrm{R}_{\mathrm{BC}}=\frac{20 \mathrm{x}}{10+2 \mathrm{x}}+20-\mathrm{x}+20-\mathrm{x} \quad \ldots$(i)
<br/>or $\quad \frac{20 \mathrm{x}}{10+2 \mathrm{x}}+40=2 \mathrm{x}$
<br/>Solving we get $\mathrm{x}=10 \Omega$
<br/>Putting the value of $x=10 \Omega$ in equation (i) We get $\mathrm{R}_{\mathrm{BC}}=\frac{20 \times 10}{10+2 \times 10}+20-10+20-10$
<br/>$=\frac{80}{3}=26.7 \Omega$</div>


tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch0.db
title:
A letter'A' is constructed of a uniform wire with resistance 1.0Î© per cm , The sides of the letter are 20 cm and the cross piece in the middle is 10 cm long. The apex angle is 60. The resistance between the ends of the legs is close to:

slug:
a-letter-a-is-constructed-of-a-uniform-wire-with-resistance-1-0-per-cm-the-sides-of-the-letter-62190

question:
<div class="question">A letter'A' is constructed of a uniform wire with resistance $1.0 \Omega$ per $\mathrm{cm}$, The sides of the letter are $20 \mathrm{~cm}$ and the cross piece in the middle is 10 $\mathrm{cm}$ long. The apex angle is $60 .$ The resistance between the ends of the legs is close to:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$50.0 \Omega$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 \Omega$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$36.7 \Omega$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$26.7 \Omega$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$26.7 \Omega$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Y5sbUODQvszObE9Pnn_44LN51U94r0ntiNbllSp34b8.original.fullsize.png"/><br/> <br/>For ADE $\frac{1}{R^{\prime}}=\frac{1}{2 x}+\frac{1}{10} \quad$ or $\quad R^{\prime}=\frac{20 x}{10+2 x}$
<br/>$\mathrm{R}_{\mathrm{BC}}=\frac{20 \mathrm{x}}{10+2 \mathrm{x}}+20-\mathrm{x}+20-\mathrm{x} \quad \ldots$(i)
<br/>or $\quad \frac{20 \mathrm{x}}{10+2 \mathrm{x}}+40=2 \mathrm{x}$
<br/>Solving we get $\mathrm{x}=10 \Omega$
<br/>Putting the value of $x=10 \Omega$ in equation (i) We get $\mathrm{R}_{\mathrm{BC}}=\frac{20 \times 10}{10+2 \times 10}+20-10+20-10$
<br/>$=\frac{80}{3}=26.7 \Omega$</div>


tags: ['Physics', 'Dual Nature of Matter', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch0.db
title:
A light having wavelength 300 nm fall on a metal surface. The work function of metal is 2.54 eV , what is stopping potential?

slug:
a-light-having-wavelength-300-nm-fall-on-a-metal-surface-the-work-function-of-metal-is-2-54-ev-wh-71640

question:
<div class="question">A light having wavelength $300 \mathrm{nm}$ fall on a metal surface. The work function of metal is $2.54 \mathrm{eV}$, what is stopping potential?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2.3 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2.59 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1.59 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1.29 \mathrm{~V}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.59 \mathrm{~V}$</span> </div>

answer:
<div class="solution">Energy of incident radiation is given by:
<br/>\(\mathrm{E}=\frac{\mathrm{hc}}{\lambda}=\frac{6.64 * 10^{-34} * 3 * 10^{8}}{300 * 10^{-9}}=6.64 * 10^{-19}=4.05 \mathrm{eV}\)
<br/>The work function of the metal is equal to \(2.54 \mathrm{eV}\)
<br/>Hence the maximum kinetic energy of an ejected photoelectron would be \(1.59 \mathrm{eV}\)
<br/>And the stopping potential needed to stop this would be \(1.59 \mathrm{~V}\).</div>


tags: ['Physics', 'Work Power Energy', 'JEE Main']
source_db: MarksBatch0.db
title:
A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg . Taking g = 10 m / s 2 , find the work done ( in joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.

slug:
a-light-inextensible-string-that-goes-over-a-smooth-fixed-pulley-as-shown-in-the-figure-connects-two-93703

question:
<div class="question">A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $0.36 \mathrm{~kg}$ and $0.72 \mathrm{~kg}$. Taking $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2},$ find the work done $(\mathrm{in}$
<br/> <br/>joules) by the string on the block of mass $0.36 \mathrm{~kg}$ during the first second after the system is released from rest.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/i7gKSnXmc1MN1Q3bNmoSV1vXdMYrIOUkiYHPtD9sntw.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \mathrm{~J}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$8 \mathrm{~J}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10 \mathrm{~J}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$8 \mathrm{~J}$</span> </div>

answer:
<div class="solution">Given $m=0.36 \mathrm{~kg}, M=0.72 \mathrm{~kg}$. The figure shows the forces on $m$ and $M$. When the system is released, let the acceleration be $a$. Then
<br/> <br/>$T-m g=m a$
<br/> <br/>$M g-T=M a$
<br/> <br/>$$
<br/> <br/>a=\frac{(M-m) g}{M+m}=g / 3
<br/> <br/>$$
<br/> <br/>and $T=4 \mathrm{mg} / 3$
<br/> <br/>For block m:
<br/> <br/>$$
<br/> <br/>u=0, a=g / 3, t=1, s=?
<br/> <br/>$$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/_LD6QYhzhQSmiBzK3EKnfY0Rr12eqtvfzy_3HP0QUNg.original.fullsize.png"/><br/> <br/> <br/>$$
<br/> <br/>s=u t+\frac{1}{2} a t^{2}=0+\frac{1}{2} \times \frac{g}{3} \times 1^{2}=g / 6
<br/> <br/>$$
<br/> <br/>Work done by the string on $m$ is
<br/> <br/>$$
<br/> <br/>\bar{T} \bar{s}=T s=4 \frac{m g}{3} \times \frac{g}{6}=\frac{4 \times 0.36 \times 10 \times 10}{3 \times 6}=8 \mathrm{~J}
<br/> <br/>$$</div>


tags: ['Physics', 'Work Power Energy', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch0.db
title:
A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg . Taking g = 10 m / s 2 , find the work done ( in joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.

slug:
a-light-inextensible-string-that-goes-over-a-smooth-fixed-pulley-as-shown-in-the-figure-connects-two-95181

question:
<div class="question">A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $0.36 \mathrm{~kg}$ and $0.72 \mathrm{~kg}$. Taking $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2},$ find the work done $(\mathrm{in}$
<br/> <br/>joules) by the string on the block of mass $0.36 \mathrm{~kg}$ during the first second after the system is released from rest.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/i7gKSnXmc1MN1Q3bNmoSV1vXdMYrIOUkiYHPtD9sntw.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \mathrm{~J}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$8 \mathrm{~J}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10 \mathrm{~J}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$8 \mathrm{~J}$</span> </div>

answer:
<div class="solution">Given $m=0.36 \mathrm{~kg}, M=0.72 \mathrm{~kg}$. The figure shows the forces on $m$ and $M$. When the system is released, let the acceleration be $a$. Then
<br/> <br/>$T-m g=m a$
<br/> <br/>$M g-T=M a$
<br/> <br/>$$
<br/> <br/>a=\frac{(M-m) g}{M+m}=g / 3
<br/> <br/>$$
<br/> <br/>and $T=4 \mathrm{mg} / 3$
<br/> <br/>For block m:
<br/> <br/>$$
<br/> <br/>u=0, a=g / 3, t=1, s=?
<br/> <br/>$$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/_LD6QYhzhQSmiBzK3EKnfY0Rr12eqtvfzy_3HP0QUNg.original.fullsize.png"/><br/> <br/> <br/>$$
<br/> <br/>s=u t+\frac{1}{2} a t^{2}=0+\frac{1}{2} \times \frac{g}{3} \times 1^{2}=g / 6
<br/> <br/>$$
<br/> <br/>Work done by the string on $m$ is
<br/> <br/>$$
<br/> <br/>\bar{T} \bar{s}=T s=4 \frac{m g}{3} \times \frac{g}{6}=\frac{4 \times 0.36 \times 10 \times 10}{3 \times 6}=8 \mathrm{~J}
<br/> <br/>$$</div>


slug: a-line-makes-angles-of-4-5-and-6-0-with-the-positive-axes-of-x-and-y-respectively-the-angle-38960
tags: ['Mathematics', 'Three Dimensional Geometry', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch0.db
title:
A line makes angles of 4 5 â and 6 0 â with the positive axes of X and Y respectively. The angle made by the same line with the positive axis of Z , is

question:
<div class="question">A line makes angles of $45^{\circ}$ and $60^{\circ}$ with the positive axes of $X$ and $Y$ respectively. The angle made by the same line with the positive axis of $Z$, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$30^{\circ}$ or $60^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$60^{\circ}$ or $90^{\circ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$90^{\circ}$ or $120^{\circ}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$60^{\circ}$ or $120^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$60^{\circ}$ or $120^{\circ}$</span> </div>

answer:
<div class="solution">Given $\alpha=45^{\circ}, \beta=60^{\circ}, \gamma=?$
<br/> <br/>$\begin{array}{l}
<br/> <br/>\because \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \\
<br/> <br/>\therefore \cos ^{2} \gamma=1-\frac{1}{2}-\frac{1}{4}=\frac{1}{4} \\
<br/> <br/>\Rightarrow \mathrm{y}=60^{\circ} \text { or } 120^{\circ}
<br/> <br/>\end{array}$</div>


slug: a-line-makes-angles-with-the-coordinate-axes-if-2-then-cos-cos-69625
tags: ['Mathematics', 'Three Dimensional Geometry', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch0.db
title:
A line makes angles Î± , Î² , Î³ with the coordinate axes. If Î± + Î² = Ï 2 , then cos Î± + cos Î² + cos Î³ 2 is equal to

question:
<div class="question">A line makes angles <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>,</mo><mo> </mo><mi>β</mi><mo>,</mo><mo> </mo><mi>γ</mi></math> with the coordinate axes. If <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>+</mo><mi>β</mi><mo>=</mo><mfrac><mi>π</mi><mn>2</mn></mfrac></math>, then <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>cos</mi><mi>α</mi><mo>+</mo><mi>cos</mi><mi>β</mi><mo>+</mo><mi>cos</mi><mi>γ</mi></mrow></mfenced><mn>2</mn></msup></math> is equal to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>+</mo><mi>sin</mi><mn>2</mn><mi>α</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mi>sin</mi><mn>2</mn><mi>α</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>+</mo><mi>cos</mi><mn>2</mn><mi>α</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>+</mo><mi>sin</mi><mn>2</mn><mi>α</mi></math></span> </div>

answer:
<div class="solution"><p>We have, <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>cos</mi><mn>2</mn></msup><mi>α</mi><mo>+</mo><msup><mi>cos</mi><mn>2</mn></msup><mi>β</mi><mo>+</mo><msup><mi>cos</mi><mn>2</mn></msup><mi>γ</mi><mo>=</mo><mn>1</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>cos</mi><mn>2</mn></msup><mi>α</mi><mo>+</mo><msup><mi>cos</mi><mn>2</mn></msup><mfenced><mrow><mfrac><mi>π</mi><mn>2</mn></mfrac><mo>-</mo><mi>α</mi></mrow></mfenced><mo>+</mo><msup><mi>cos</mi><mn>2</mn></msup><mi>γ</mi><mo>=</mo><mn>1</mn></math>  [given <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>+</mo><mi>β</mi><mo>=</mo><mfrac><mi>π</mi><mn>2</mn></mfrac></math>]</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>cos</mi><mn>2</mn></msup><mi>α</mi><mo>+</mo><msup><mi>sin</mi><mn>2</mn></msup><mi>α</mi><mo>+</mo><msup><mi>cos</mi><mn>2</mn></msup><mi>γ</mi><mo>=</mo><mn>1</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mn>1</mn><mo>+</mo><msup><mi>cos</mi><mn>2</mn></msup><mi>γ</mi><mo>=</mo><mn>1</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>cos</mi><mn>2</mn></msup><mi>γ</mi><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>cos</mi><mi>γ</mi><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><msup><mfenced><mrow><mi>cos</mi><mi>α</mi><mo>+</mo><mi>cos</mi><mi>β</mi><mo>+</mo><mi>cos</mi><mi>γ</mi></mrow></mfenced><mn>2</mn></msup><mo>=</mo><msup><mfenced><mrow><mi>cos</mi><mi>α</mi><mo>+</mo><mi>sin</mi><mi>α</mi></mrow></mfenced><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>+</mo><mn>2</mn><mi>sin</mi><mi>α</mi><mo>·</mo><mi>cos</mi><mi>α</mi><mo>=</mo><mn>1</mn><mo>+</mo><mi>sin</mi><mn>2</mn><mi>α</mi></math></p></div>


slug: a-line-makes-the-same-angle-with-each-of-the-x-and-z-axes-if-the-angle-which-it-makes-with-34474
tags: ['Mathematics', 'Three Dimensional Geometry', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch0.db
title:
A line makes the same angle Î¸ with each of the X and Z -axes. If the angle Î² , which it makes with Y-axis, is such that sin 2 Î² = 3 sin 2 Î¸ , then cos 2 Î¸ equals

question:
<div class="question">A line makes the same angle $\theta$ with each of the $\mathrm{X}$ and $\mathrm{Z}$ -axes. If the angle $\beta$, which it makes with Y-axis, is such that $\sin ^{2} \beta=3 \sin ^{2} \theta,$ then $\cos ^{2} \theta$ equals</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 / 5$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1 / 5$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$3 / 5$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 / 3$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3 / 5$</span> </div>

answer:
<div class="solution">Let $l, \mathrm{~m}$ and $\mathrm{n}$ be the direction cosines. Then, $l=\cos \theta, \mathrm{m}=\cos \beta, \mathrm{n}=\cos \theta$
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\text { we have } l^{2}+m^{2}+n^{2}=1 \\
<br/> <br/>\Rightarrow \cos ^{2} \theta+\cos ^{2} \beta+\cos ^{2} \theta=1 \\
<br/> <br/>\Rightarrow 2 \cos ^{2} \theta+1-\sin ^{2} \beta=1 \\
<br/> <br/>\Rightarrow 2 \cos ^{2} \theta-\sin ^{2} \beta=0 \\
<br/> <br/>\Rightarrow 2 \cos ^{2} \theta-3 \sin ^{2} \beta=0 \\
<br/> <br/>\quad\left[\because \sin ^{2} \beta=3 \sin ^{2} 0(\text { given })\right] \\
<br/> <br/>\Rightarrow \tan ^{2} \theta=2 / 3 \\
<br/> <br/>\therefore \cos ^{2} \theta=\frac{1}{1+\tan ^{2} \theta}=\frac{1}{1+2 / 3}=\frac{3}{5}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


slug: a-line-segment-has-length-63-and-direction-ratios-are-3-2-6-if-the-line-makes-an-obtuse-angle-69951
tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch0.db
title:
A line segment has length 63 and direction ratios are \(3,-2,6\). If the line makes an obtuse angle with \(\mathrm{x}\)-axis, the components of the line vector are

question:
<div class="question">A line segment has length 63 and direction ratios are \(3,-2,6\). If the line makes an obtuse angle with \(\mathrm{x}\)-axis, the components of the line vector are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(27,-18,54\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(-27,18,54\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(-27,18,-54\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(27,-18,-54\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(-27,18,-54\)</span> </div>

answer:
<div class="solution">Let the components of the line vector be a, b, c. Then \(\mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2=(63)^2\) ...(i)<br/>Also \(\frac{\mathrm{a}}{3}=\frac{\mathrm{b}}{-2}=\frac{\mathrm{c}}{6}=\lambda\) (say), then \(\mathrm{a}=3 \lambda\), \(\mathrm{b}=-2 \lambda\) and \(\mathrm{c}=6 \lambda\) and from (i) we have \(9 \lambda^2+4 \lambda^2+36 \lambda^2=(63)^2\)<br/>\(\Rightarrow 49 \lambda^2=(63)^2\)<br/>\(\Rightarrow \lambda= \pm \frac{63}{7}= \pm 9\)<br/>Since \(a=3 \lambda  &lt; 0\) as the line makes an obtuse angle with \(x\)-axis, \(\lambda=-9\) and the required components are \(-27,18,-54\).</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch0.db
title:
A liquid is flowing through a non-sectional tube with its axis horizontally. If two points X and Y on the axis of tube has a sectional area 2.0 cm 3 and 25 mm 2 respectively then find the flow velocity at Y when the flow velocity at X is 10 m / s .

slug:
a-liquid-is-flowing-through-a-non-sectional-tube-with-its-axis-horizontally-if-two-points-x-and-y-o-44229

question:
<div class="question">A liquid is flowing through a non-sectional tube with its axis horizontally. If two points $\mathrm{X}$ and $\mathrm{Y}$ on the axis of tube has a sectional area $2.0 \mathrm{~cm}^{3}$ and $25 \mathrm{~mm}^{2}$ respectively then find the flow velocity at $Y$ when the flow velocity at $X$ is $10 \mathrm{~m} / \mathrm{s}$.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$20 \mathrm{~m} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$40 \mathrm{~m} / \mathrm{s}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$80 \mathrm{~m} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$60 \mathrm{~m} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$80 \mathrm{~m} / \mathrm{s}$</span> </div>

answer:
<div class="solution">According to principle of continuity<br/>$$<br/>v_{y}=\frac{v_{x} A_{x}}{A_{y}}=\frac{10(m / s) \times 2\left(c m^{2}\right)}{25 \times 10^{-2}\left(c m^{2}\right)}=80 \mathrm{~m} / \mathrm{s}<br/>$$</div>


tags: ['Physics', 'Oscillations', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch0.db
title:
A load of mass m falls from a height h on the scale pan hung from a spring as shown. If the spring constant is k and the mass of the scale pan is zero and the mass m does not bounce relative to the pan, then the amplitude of vibration is

slug:
a-load-of-mass-m-falls-from-a-height-h-on-the-scale-pan-hung-from-a-spring-as-shown-if-the-spring-c-53341

question:
<div class="question"><p>A load of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> falls from a height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> on the scale pan hung from a spring as shown. If the spring constant is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> and the mass of the scale pan is zero and the mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> does not bounce relative to the pan, then the amplitude of vibration is </p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/a5eae703-e0ed-4086-92f2-856e6fc9b23a-image.png" style="width: 200px; height: 306px;"/></p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac><msqrt><mn>1</mn><mo>+</mo><mfrac><mrow><mn>2</mn><mi>h</mi><mi>k</mi></mrow><mrow><mi>m</mi><mi>g</mi></mrow></mfrac></msqrt></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac><mo>+</mo><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac><msqrt><mfrac><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>h</mi><mi>k</mi></mrow><mrow><mi>m</mi><mi>g</mi></mrow></mfrac></msqrt></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac><msqrt><mn>1</mn><mo>+</mo><mfrac><mrow><mn>2</mn><mi>h</mi><mi>k</mi></mrow><mrow><mi>m</mi><mi>g</mi></mrow></mfrac></msqrt></math></span> </div>

answer:
<div class="solution"><p>From the energy conservation principle,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>g</mi><mi>h</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>k</mi><msubsup><mi>X</mi><mn>0</mn><mn>2</mn></msubsup><mo>-</mo><mi>m</mi><mi>g</mi><msub><mi>X</mi><mn>0</mn></msub></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mn>0</mn></msub></math> is maximum elongation in spring.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>k</mi><msubsup><mi>X</mi><mn>0</mn><mn>2</mn></msubsup><mo>-</mo><mi>m</mi><mi>g</mi><msub><mi>X</mi><mn>0</mn></msub><mo>-</mo><mi>m</mi><mi>g</mi><mi>h</mi><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msubsup><mi>X</mi><mn>0</mn><mn>2</mn></msubsup><mo>-</mo><mfrac><mrow><mn>2</mn><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac><msub><mi>X</mi><mn>0</mn></msub><mo>-</mo><mfrac><mrow><mn>2</mn><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac><mi>h</mi><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mn>0</mn></msub><mo>=</mo><mfrac><mrow><mn>2</mn><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mn>2</mn></mfrac><mo>±</mo><msqrt><msup><mfenced><mfrac><mrow><mn>2</mn><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac></mfenced><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>×</mo><mfrac><mrow><mn>2</mn><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac><mi>h</mi></msqrt></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mn>2</mn></mfrac><mo>+</mo><msqrt><msup><mfenced><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac></mfenced><mn>2</mn></msup><mo>+</mo><mfrac><mrow><mn>2</mn><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac><mi>h</mi></msqrt></math></p><p>Amplitude <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math> elongation in spring for lowest extreme position<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>X</mi><mn>0</mn></msub></mfenced></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math> elongation in spring for equilibrium position<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>X</mi><mn>1</mn></msub></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msub><mi>X</mi><mn>0</mn></msub><mo>-</mo><msub><mi>X</mi><mn>1</mn></msub><mo>=</mo><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac><msqrt><mn>1</mn><mo>+</mo><mfrac><mrow><mn>2</mn><mi>h</mi><mi>k</mi></mrow><mrow><mi>m</mi><mi>g</mi></mrow></mfrac></msqrt><mo> </mo></math>,   <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>∵</mo><msub><mi>X</mi><mn>1</mn></msub><mo>=</mo><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mi>k</mi></mfrac></mrow></mfenced></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch0.db
title:
A load of mass m falls from a height h on to the scale pan hung from the spring as shown in the figure. If the spring constant is k and mass of the scale pan is zero and the mass m does not bounce relative to the pan, then the amplitude of vibration is

slug:
a-load-of-mass-m-falls-from-a-height-h-on-to-the-scale-pan-hung-from-the-spring-as-shown-in-the-figu-98237

question:
<div class="question">A load of mass m falls from a height h on to the scale pan hung from the spring as shown in the figure. If the spring constant is $\mathrm{k}$ and mass of the scale pan is zero and the mass $\mathrm{m}$ does not bounce relative to the pan, then the amplitude of vibration is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/MII3jxvI459IXuFrqsqf4QInRZ3xrVDaHO7VyWKbHHU.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{mg} / \mathrm{d}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\mathrm{mg}}{\mathrm{k}} \sqrt{\left(\frac{1+2 \mathrm{hk}}{\mathrm{mg}}\right)}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{mg}}{\mathrm{k}}+\frac{\mathrm{mg}}{\mathrm{k}} \sqrt{\left(\frac{1+2 \mathrm{hk}}{\mathrm{mg}}\right)}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mathrm{mg}}{\mathrm{k}} \sqrt{\left(\frac{1+2 \mathrm{hk}}{\mathrm{mg}}-\frac{\mathrm{mg}}{\mathrm{k}}\right)}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{mg}}{\mathrm{k}} \sqrt{\left(\frac{1+2 \mathrm{hk}}{\mathrm{mg}}\right)}$</span> </div>

answer:
<div class="solution">According to energy conservation principle, If, $\mathrm{x}_{1}$ is maximum elongation in the spring when the particle is in its lowest extreme position. Then,
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\mathrm{mgh}=\frac{1}{2} \mathrm{kx}_{1}^{2}-\mathrm{mgx}_{1} \\
<br/> <br/>\Rightarrow \frac{1}{2} \mathrm{kx}_{1}^{2}-\mathrm{mgx}_{1}-\mathrm{mgh}=0 \\
<br/> <br/>\text { or, } \mathrm{x}_{1}^{2}-\frac{2 \mathrm{mg}}{\mathrm{k}} \mathrm{x}_{1}-\frac{2 \mathrm{mg}}{\mathrm{k}} \cdot \mathrm{h}=0 \\
<br/> <br/>\therefore \mathrm{x}_{1}=\frac{\frac{2 \mathrm{mg}}{\mathrm{k}} \pm \sqrt{\left.\left(\frac{2 \mathrm{mg}}{\mathrm{k}}\right)^{2}+4 \times \frac{2 \mathrm{mg}}{\mathrm{k}} \mathrm{h}\right]}}{2}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Amplitude $\mathrm{A}=\mathrm{X}_{1}-\mathrm{X}_{0}$ (elongation in spring for equilibrium position)
<br/> <br/>$$
<br/> <br/>\mathrm{A}=\frac{\mathrm{mg}}{\mathrm{k}} \sqrt{\left(1+\frac{2 \mathrm{hk}}{\mathrm{mg}}\right)}
<br/> <br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch0.db
title:
A long straight wire along the Z -axis carries a current I in the negative Z -direction. The magnetic vector field B at a point having coordinates ( x , y ) in the Z = 0 plane is

slug:
a-long-straight-wire-along-the-z-axis-carries-a-current-i-in-the-negative-z-direction-the-magneti-23262

question:
<div class="question">A long straight wire along the $Z$ -axis carries a current I in the negative $Z$ -direction. The
<br/> <br/>magnetic vector field $\vec{B}$ at a point having coordinates $(x, y)$ in the $Z=0$ plane is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{\mu_{0} I(y \hat{i}-x \hat{j})}{2 \pi\left(x^{2}+y^{2}\right)}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\mu_{0} I(x \hat{i}+y \hat{j})}{2 \pi\left(x^{2}+y^{2}\right)}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mu_{0} I(x \hat{j}-y \hat{i})}{2 \pi\left(x^{2}+y^{2}\right)}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mu_{0} I(x \hat{i}-y \hat{j})}{2 \pi\left(x^{2}+y^{2}\right)}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mu_{0} I(y \hat{i}-x \hat{j})}{2 \pi\left(x^{2}+y^{2}\right)}$</span> </div>

answer:
<div class="solution">The wire carries a current $I$ in the negative $z$ -direction. We have to consider the
<br/> <br/>magnetic vector field $\vec{B}$ at $(x, y)$ in the $z=0$ plane.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/USmKK_7_XG-H5CPMkrNdWUbIbHIBnjlAwdJk7tBK1OY.original.fullsize.png"/><br/> <br/> <br/>Magnetic field $\vec{B}$ is perpendicular to $O P$ $\therefore \vec{B}=B \sin \theta \hat{i}-B \cos \theta \hat{j}$
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\sin \theta=\frac{y}{r}, \cos \theta=\frac{x}{r} B=\frac{\mu_{0} I}{2 \pi r} \\
<br/> <br/>\therefore \quad \vec{B}=\frac{\mu_{0} I}{2 \pi r^{2}}(y \hat{i}-x \hat{j})
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>or $\quad \vec{B}=\frac{\mu_{0} I(y \hat{i}-x \hat{j})}{2 \pi\left(x^{2}+y^{2}\right)}$</div>


tags: ['Physics', 'Work Power Energy', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch0.db
title:
A long string is stretched by 2 cm and the potential energy is V . If the spring is stretched by 10 cm , its potential energy will be

slug:
a-long-string-is-stretched-by-2-cm-and-the-potential-energy-is-v-if-the-spring-is-stretched-by-10-42374

question:
<div class="question">A long string is stretched by $2 \mathrm{~cm}$ and the potential energy is $\mathrm{V}$. If the spring is stretched by $10 \mathrm{~cm}$, its potential energy will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{V} / 25$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{V} / 5$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$5 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$25 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$25 \mathrm{~V}$</span> </div>

answer:
<div class="solution">$\quad V=\frac{1}{2} k(x)^{2}=\frac{1}{2} k(2)^{2}$ or $k=\frac{2 V}{4}=\frac{V}{2}$<br/>$$<br/>\mathrm{V}^{\prime}=\frac{1}{2} \mathrm{k}(10)^{2}=\frac{1}{2} \times\left(\frac{\mathrm{V}}{2}\right)(10)^{2}=25 \mathrm{~V}<br/>$$</div>


tags: ['Chemistry', 'Solutions', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P1.db
title:
100-g-of-a-nonelectrolyte-solute-molar-mass-250-g-mol-1-was-dissolved-in-512-g-of-benzene-if-the-freezing-point-depression-constant-k-f-of-benzene-is-

slug:
100-g-of-a-nonelectrolyte-solute-molar-mass-250-g-mol-1-was-dissolved-in-512-g-of-benzene-if-the-freezing-point-depression-constant-k-f-of-benzene-is-90177

question:
<div class="question">$1.00 \mathrm{~g}$ of a non-electrolyte solute (molar mass $\left.250 \mathrm{~g} \mathrm{~mol}^{-1}\right)$ was dissolved in $51.2 \mathrm{~g}$ of benzene. If the freezing point depression constant, $\mathrm{K}_{\mathrm{f}}$ of benzene is $5.12 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$, the freezing point of benzene will be lowered by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.3 \mathrm{~K}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.5 \mathrm{~K}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$0.4 \mathrm{~K}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0.2</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.4 \mathrm{~K}$</span> </div>

answer:
<div class="solution">$\Delta \mathrm{T}_{\mathrm{f}}=\mathrm{K}_{\mathrm{f}} \mathrm{m}=5.12 \times \frac{1}{250} \times \frac{1000}{51.2}=0.4 \mathrm{~K}$</div>


tags: ['Mathematics', 'Vector Algebra', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch1_P1.db
title:
107-u-and-v-are-two-noncollinear-unit-vectors-such-that-2-u-v-u-v-1-then-the-value-of-u-v-is-equal-to

slug:
107-u-and-v-are-two-noncollinear-unit-vectors-such-that-2-u-v-u-v-1-then-the-value-of-u-v-is-equal-to-74203

question:
<div class="question">107. $\hat{\mathbf{u}}$ and $\hat{\mathbf{v}}$ are two non-collinear unit vectors such that $\left|\frac{\hat{\mathbf{u}}+\hat{\mathbf{v}}}{\mathbf{2}}+\hat{\mathbf{u}} \times \hat{\mathbf{v}}\right|=1$. Then the value of $|\hat{\mathbf{u}} \times \hat{\mathbf{v}}|$ is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$\left|\frac{\hat{\mathbf{u}}+\hat{\mathbf{v}}}{2}\right|$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$|\hat{\mathbf{u}}+\hat{\mathbf{v}}|$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$|\hat{\mathbf{u}}-\hat{\mathbf{v}}|$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>$\left|\frac{\hat{\mathbf{u}}-\hat{\mathbf{v}}}{2}\right|$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$\left|\frac{\hat{\mathbf{u}}-\hat{\mathbf{v}}}{2}\right|$</span> </div>

answer:
<div class="solution">Given that, $\left|\frac{\hat{\mathbf{u}}+\hat{\mathbf{v}}}{2}+\hat{\mathbf{u}} \times \hat{\mathbf{v}}\right|=1$
<br/>$$
<br/>\begin{array}{ll}
<br/>\Rightarrow &amp; \left|\frac{\hat{\mathbf{u}}+\hat{\mathbf{v}}}{2}+\hat{\mathbf{u}} \times \hat{\mathbf{v}}\right|^2=1 \\
<br/>\Rightarrow &amp; \frac{2+2 \cos \theta}{4}+\sin ^2 \theta=1 \\
<br/> &amp; \quad[\because \hat{\mathbf{u}} \cdot(\hat{\mathbf{u}} \times \hat{\mathbf{v}})=\hat{\mathbf{v}}(\hat{\mathbf{u}} \times \hat{\mathbf{v}})=0] \\
<br/>\Rightarrow &amp; \cos ^2 \frac{\theta}{2}=\cos 2 \theta \\
<br/>\Rightarrow &amp; \theta=n \pi \pm \frac{\theta}{2}, n \in z \\
<br/>\Rightarrow &amp; \theta=\frac{2 \pi}{3}
<br/>\end{array}
<br/>$$
<br/>$\Rightarrow \quad|\hat{\mathbf{u}} \times \hat{\mathbf{v}}|=\sin \frac{2 \pi}{3}=\sin \frac{\pi}{3}=\left|\frac{\hat{\mathbf{u}}-\hat{\mathbf{v}}}{2}\right|$</div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P1.db
title:
125-g-of-a-sample-of-na-2-co-3-and-na-2-so-4-is-dissolved-in-250-ml-solution-25-ml-of-this-solution-neutralises-20-ml-of-01-n-h-2-so-4-the-of-na-2-co-

slug:
125-g-of-a-sample-of-na-2-co-3-and-na-2-so-4-is-dissolved-in-250-ml-solution-25-ml-of-this-solution-neutralises-20-ml-of-01-n-h-2-so-4-the-of-na-2-co-20834

question:
<div class="question">$1.25 \mathrm{~g}$ of a sample of $\mathrm{Na}_{2} \mathrm{CO}_{3}$ and $\mathrm{Na}_{2} \mathrm{SO}_{4}$ is
<br/> <br/>dissolved in $250 \mathrm{ml}$ solution. $25 \mathrm{ml}$ of this solution neutralises $20 \mathrm{ml}$ of $0.1 \mathrm{~N} \mathrm{H}_{2} \mathrm{SO}_{4}$. The $\%$ of $\mathrm{Na}_{2} \mathrm{CO}_{3}$
<br/> <br/>in this sample is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$84.8 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$8.48 \%$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$15.2 \%$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$42.4 \%$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$84.8 \%$</span> </div>

answer:
<div class="solution">Let the amount of $\mathrm{Na}_{2} \mathrm{CO}_{3}$ present in the mixture be $\mathrm{xg} . \mathrm{Na}_{2} \mathrm{SO}_{4}$ will not react with $\mathrm{H}_{2} \mathrm{SO}_{4} .$ Then
<br/> <br/>$\frac{x}{53}=\frac{20 \times 0.1 \times 10}{1000} \therefore x=1.06 g$
<br/> <br/>$\therefore$ Percentage of $\mathrm{Na}_{2} \mathrm{CO}_{3}=$
<br/> <br/>$\frac{1.06 \times 100}{1.25}=84.8 \%$</div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">50</span> </div>
source_db: MarksBatch1_P1.db
title:
392-g-of-ferrous-ammonium-sulphate-react-completely-with-50-ml-10-n-kmno-4-solution-the-percentage-purity-of-the-sample-is

slug:
392-g-of-ferrous-ammonium-sulphate-react-completely-with-50-ml-10-n-kmno-4-solution-the-percentage-purity-of-the-sample-is-23367

question:
<div class="question">$3.92 \mathrm{~g}$ of ferrous ammonium sulphate react completely with $50 \mathrm{ml} \frac{\mathrm{N}}{10} \mathrm{KMnO}_{4}$ solution. The percentage purity of the sample is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">50</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">78.4</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">80</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">39.2</span> </li> </ul>

answer:
<div class="solution">Eq of $\mathrm{KMnO}_{4}$ used $=\frac{50 \times 1}{1000 \times 10}=0.005$
<br/> <br/>$\therefore$ Eq of FAS reacted $=0.005$
<br/> <br/>$\therefore$ weight of FAS needed
<br/> <br/>$$
<br/> <br/>=0.005 \times 392=1.96 \mathrm{~g}
<br/> <br/>$$
<br/> <br/>Thus percentage purity of FAS is $50 \%$</div>


title: 1520-g-of-hydroxide-of-a-metal-on-ignition-gave-0995-g-of-oxide-the-equivalent-weight-of-metal-is
tags: ['Chemistry', 'Redox Reactions', 'BITSAT', 'BITSAT 2011']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9</span> </div>
source_db: MarksBatch1_P1.db
slug:
1520-g-of-hydroxide-of-a-metal-on-ignition-gave-0995-g-of-oxide-the-equivalent-weight-of-metal-is-62274

question:
<div class="question">$1.520 \mathrm{~g}$ of hydroxide of a metal on ignition gave $0.995 \mathrm{~g}$ of oxide. The equivalent weight of metal is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1.52</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0.995</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">190</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">9</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Let $E$ be the equivalent weight of the metal<br/>$$<br/>\text { So, } \frac{E+17}{E+8}=\frac{1.52}{0.995}<br/>$$<br/>[17 is equivalent weight of $\mathrm{OH}$ and 8 is equivalent weight of oxygen]<br/>$$<br/>\begin{array}{l}<br/>\Rightarrow 0.995 \mathrm{E}+17 \times 0.995=\mathrm{E} \times 1.52+8 \times 1.52 \\<br/>\Rightarrow 0.525 \mathrm{E}=16.915-12.16=4.755 \\<br/>\therefore \quad \mathrm{E}=\frac{4.755}{0.525}=9<br/>\end{array}<br/>$$</div>


tags: ['Physics', 'Oscillations', 'BITSAT', 'BITSAT 2016']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch1_P1.db
title:
a-1-kg-mass-is-attached-to-a-spring-of-force-constant-600-n-m-and-rests-on-a-smooth-horizontal-surface-with-other-end-of-the-spring-tied-to-wall-as-sh

slug:
a-1-kg-mass-is-attached-to-a-spring-of-force-constant-600-n-m-and-rests-on-a-smooth-horizontal-surface-with-other-end-of-the-spring-tied-to-wall-as-sh-49965

question:
<div class="question">A $1 \mathrm{~kg}$ mass is attached to a spring of force constant $600 \mathrm{~N} / \mathrm{m}$ and rests on a smooth horizontal surface with other end of the spring tied to wall as shown in figure. A second mass of $0.5 \mathrm{~kg}$ slides along the surface towards the first at $3 \mathrm{~m} / \mathrm{s}$. If the masses make a perfectly inelastic collision, then find amplitude and time period of oscillation of combined mass.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/7RB8kg5GImmHiuCU5XdGpoGOppt6O5xpyJtDsUB4MYA.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$5 \mathrm{~cm}, \frac{\pi}{10} \mathrm{~s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5 \mathrm{~cm}, \frac{\pi}{5} \mathrm{~s}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4 \mathrm{~cm}, \frac{2 \pi}{5} \mathrm{~s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4 \mathrm{~cm}, \frac{\pi}{3} \mathrm{~s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$5 \mathrm{~cm}, \frac{\pi}{10} \mathrm{~s}$</span> </div>


tags: ['Physics', 'Motion In Two Dimensions', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch1_P1.db
title:
a-2-m-wide-truck-is-moving-with-a-uniform-speed-v-0-8-m-s-along-a-straight-horizontal-road-a-pedestrain-starts-to-cross-the-road-with-a-uniform-speed-

slug:
a-2-m-wide-truck-is-moving-with-a-uniform-speed-v-0-8-m-s-along-a-straight-horizontal-road-a-pedestrain-starts-to-cross-the-road-with-a-uniform-speed-61547

question:
<div class="question">A $2 \mathrm{~m}$ wide truck is moving with a uniform speed $v_{0}=8 \mathrm{~m} / \mathrm{s}$ along a straight horizontal road. $\mathrm{A}$ pedestrain starts to cross the road with a uniform speed $v$ when the truck is 4 m away from him. The minimum value of $v$ so that he can cross the road safely is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Z3fJLaj1dg6v6X8HIQc2GSDfUqbDQP6LBa9-0HbyYFE.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2.62 \mathrm{~m} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4.6 \mathrm{~m} / \mathrm{s}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$3.57 \mathrm{~m} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1.414 \mathrm{~m} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3.57 \mathrm{~m} / \mathrm{s}$</span> </div>

answer:
<div class="solution">Let the man starts crossing the road at an angle $\theta$ as shown in figure. For safe crossing the condition is that the man must cross the road by the time the truck describes the distance 4 à¥¤ $A C$ or 4 à¥¤ $2 \cot \theta$. $\therefore \frac{4+2 \cot \theta}{8}=\frac{2 / \sin \theta}{v}$ or $v=\frac{8}{2 \sin \theta+\cos \theta}$
<br/> <br/>For minimum $v, \frac{d v}{d \theta}=0$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/0Fx5hXOh-RW30FnSsjhaGPlflHon3wkCwFFKFHGt6w4.original.fullsize.png"/><br/> <br/> <br/>or $\frac{-8(2 \cos \theta-\sin \theta)}{(2 \sin \theta+\cos \theta)^{2}}=0$ or $2 \cos \theta-$
<br/> <br/>$\sin \theta=0$
<br/> <br/>or $\tan \theta=2$
<br/> <br/>From equation (i),
<br/> <br/>$$
<br/> <br/>v_{\min }=\frac{8}{2\left(\frac{2}{\sqrt{5}}\right)+\frac{1}{\sqrt{5}}}=\frac{8}{\sqrt{5}}=3.57 \mathrm{~m} / \mathrm{s}
<br/> <br/>$$</div>


tags: ['Chemistry', 'Solutions', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-05-molal-solution-of-ethylene-glycol-in-water-is-used-as-coolant-in-a-car-if-the-freezing-point-constant-of-water-be-18-6-c-per-mole-the-mixture-sha

slug:
a-05-molal-solution-of-ethylene-glycol-in-water-is-used-as-coolant-in-a-car-if-the-freezing-point-constant-of-water-be-18-6-c-per-mole-the-mixture-sha-55998

question:
<div class="question">A 0.5 molal solution of ethylene glycol in water is used as coolant in a car. If the freezing point constant of water be $1.86^{\circ} \mathrm{C}$ per mole, the mixture shall freeze at</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.93^{\circ} \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$-0.93^{\circ} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.86^{\circ} \mathrm{C}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-1.86^{\circ} \mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-0.93^{\circ} \mathrm{C}$</span> </div>

answer:
<div class="solution"><br/>$\begin{aligned} &amp;\Delta T_f=K_f \times m=1.86 \times 0.5=0.93^{\circ} \mathrm{C} \text {; } \\ &amp; T_f=-0.93^{\circ} \mathrm{C}\end{aligned}$</div>


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-12-v-battery-connected-to-a-coil-of-resistance-6-through-a-switch-drives-a-constant-current-in-the-circuit-the-switch-is-opened-in-1-ms-the-emf-indu-1

slug:
a-12-v-battery-connected-to-a-coil-of-resistance-6-through-a-switch-drives-a-constant-current-in-the-circuit-the-switch-is-opened-in-1-ms-the-emf-indu-1-49010

question:
<div class="question">A $12 \mathrm{~V}$ battery connected to a coil of resistance $6 \Omega$ through a switch, drives a constant current in the circuit. The switch is opened in $1 \mathrm{~ms}$. The emf induced across the coil is $20 \mathrm{~V}$. The inductance of the coil is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 \mathrm{mH}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$12 \mathrm{mH}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$8 \mathrm{mH}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$10 \mathrm{mH}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10 \mathrm{mH}$</span> </div>

answer:
<div class="solution">Induced emf, $\varepsilon=-\mathrm{L} \frac{\mathrm{dI}}{\mathrm{dt}} \Rightarrow 20=-\mathrm{L} \frac{(0-2)}{10^{-3}}$ Hence, inductance of the coil.<br/>$\mathrm{L}=10 \mathrm{mH}$</div>


tags: ['Physics', 'Mechanical Properties of Solids', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch1_P1.db
title:
a-100-m-long-wire-having-crosssectional-area-625-1-0-4-m-2-and-youngs-modulus-is-1-0-10-nm-2-is-subjected-to-a-load-of-250-n-then-the-elongation-in-th

slug:
a-100-m-long-wire-having-crosssectional-area-625-1-0-4-m-2-and-youngs-modulus-is-1-0-10-nm-2-is-subjected-to-a-load-of-250-n-then-the-elongation-in-th-41028

question:
<div class="question">A $100 \mathrm{~m}$ long wire having cross-sectional area $6.25 \times 10^{-4} \mathrm{~m}^2$ and Young's modulus is $10^{10}$ $\mathrm{Nm}^{-2}$ is subjected to a load of $250 \mathrm{~N}$, then the elongation in the wire will be :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$6.25 \times 10^{-3} \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4 \times 10^{-4} \mathrm{~m}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$6.25 \times 10^{-6} \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$4 \times 10^{-3} \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 \times 10^{-3} \mathrm{~m}$</span> </div>

answer:
<div class="solution">$\Delta \ell=\frac{F \ell}{Y A}=\frac{250 \times 100}{10^{10} \times 6.25 \times 10^{-4}}=40 \times 10^{-4} \mathrm{~m}$<br/>$=4 \times 10^{-3} \mathrm{~m}$</div>


tags: ['Physics', 'Atomic Physics', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch1_P1.db
title:
a-125-ev-electron-beam-is-used-to-bombard-gaseous-hydrogen-at-room-temperature-the-number-of-spectral-lines-emitted-will-be

slug:
a-125-ev-electron-beam-is-used-to-bombard-gaseous-hydrogen-at-room-temperature-the-number-of-spectral-lines-emitted-will-be-21459

question:
<div class="question">A $12.5 \mathrm{eV}$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">3</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4</span> </li> </ul>

answer:
<div class="solution">If we assume electron in hydrogen atom takes energy $12.09 \mathrm{eV}$ from the incoming radiation, the maximum excited state of electron will be $n=3$. So, number of spectral lines is $\frac{3(3-1)}{2}=3$.<br/>Here we assume some part of energy $12.5 \mathrm{eV}$ $-12.09 \mathrm{eV}=0.41 \mathrm{eV}$ get lost due to collision.</div>


tags: ['Physics', 'Work Power Energy', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P1.db
title:
a-3628-kg-freight-car-moving-along-a-horizontal-rail-road-spur-track-at-72-km-hour-strikes-a-bumper-whose-coil-springs-experiences-a-maximum-compressi

slug:
a-3628-kg-freight-car-moving-along-a-horizontal-rail-road-spur-track-at-72-km-hour-strikes-a-bumper-whose-coil-springs-experiences-a-maximum-compressi-65214

question:
<div class="question">A $3.628 \mathrm{~kg}$ freight car moving along a horizontal rail road spur track at $7.2 \mathrm{~km} /$ hour strikes a bumper whose coil springs experiences a maximum compression of $30 \mathrm{~cm}$ in stopping the car. The elastic potential energy of the springs at the instant when they are compressed $15 \mathrm{~cm}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$12.1 \times 10^{4} \mathrm{~J}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$121 \times 10^{4} \mathrm{~J}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1.21 \times 10^{4} \mathrm{~J}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1.21 \times 10^{6} \mathrm{~J}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.21 \times 10^{4} \mathrm{~J}$</span> </div>

answer:
<div class="solution">\(\begin{aligned} 7.2 \mathrm{~km} / \mathrm{ram} &amp;=\frac{7.2 \times \frac{5}{18} \mathrm{~m} / \mathrm{s}}{7 / 2^{2}} \\ &amp;=\frac{72 \times 5}{10 \times 18}=2 \mathrm{~m} / \mathrm{s} \end{aligned}\)
<br/> <br/>firt case EC \(\frac{1}{2} k x^{2}=\frac{1}{2} m v^{2}\) \(\Rightarrow \frac{1}{7} k\left(30 \times 10^{-2}\right)^{2}=\frac{1}{2} \times 3.628 \times(2)^{2}\) \(k=\frac{4 \times 3.628}{9 \times 10^{-2}}\)
<br/> <br/>\(\begin{aligned} \text { EC } &amp; \frac{1}{2} k x^{2}=\frac{1}{2} m v^{2} \\ \Rightarrow &amp; \frac{1}{2} k\left(30 \times 10^{-2}\right)^{2}=\frac{1}{2} \times 3.628 \times(2)^{2} \\ k &amp;=\frac{4 \times 3.628}{9 \times 10^{-2}} \end{aligned}\)
<br/> <br/>energy potential enrgy when conpressed at \(15 \mathrm{~cm}\) 
<br/> <br/>\(\begin{aligned}\Rightarrow &amp; \frac{1}{2} k\left(15 \times 10^{-2}\right)^{2} \\=&amp; \frac{1}{2} \times \frac{4 \times 3.628}{9 \times 10^{-2}} \times 225 \times 10^{-4} \\=&amp; \frac{1639 \times 10^{-2}}{9} \\=&amp; 182.206 \times 10^{-2} \end{aligned}\)
<br/> <br/>\(\begin{aligned} &amp;\Rightarrow \frac{1}{2} k\left(15 \times 10^{2}\right. \\ &amp;=\frac{1}{2} \times \frac{\alpha \times 3.628}{9 \times 10^{-2}} \times 225 \times 10^{-4} \\ &amp;=\frac{1639 \times 10^{-2}}{9} \\ &amp;=182.206 \times 10^{-2} \end{aligned}\)</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2015']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">10</span> </div>
source_db: MarksBatch1_P1.db
title:
a-bag-contains-2-n-1-coins-it-is-known-that-n-of-these-coins-have-a-head-on-both-sides-whereas-the-remaining-n-1-coins-are-fair-a-coin-is-picked-up-at

slug:
a-bag-contains-2-n-1-coins-it-is-known-that-n-of-these-coins-have-a-head-on-both-sides-whereas-the-remaining-n-1-coins-are-fair-a-coin-is-picked-up-at-96714

question:
<div class="question">A bag contains $(2 n+1)$ coins. It is known that n of these coins have a head on both sides, whereas the remaining $(\mathrm{n}+1)$ coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is $31 / 42,$ then $\mathrm{n}$ is equal to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">10</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">11</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">12</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">13</span> </li> </ul>

answer:
<div class="solution">Total number of coins $=2 \mathrm{n}+1$
<br/> <br/>Consider the following events:
<br/> <br/>$\mathrm{E}_{1}=$ Getting a coin having head on both
<br/> <br/>sides from the bag.
<br/> <br/>$\mathrm{E}_{2}=$ Getting a fair coin from the bag
<br/> <br/>$\mathrm{A}=$ Toss results in a head
<br/> <br/>Given: $\mathrm{P}(\mathrm{A})=\frac{31}{42}, \mathrm{P}\left(\mathrm{E}_{1}\right)=\frac{\mathrm{n}}{2 \mathrm{n}+1}$
<br/> <br/>and $\mathrm{P}\left(\mathrm{E}_{2}\right)=\frac{\mathrm{n}+1}{2 \mathrm{n}+1}$
<br/> <br/>Then,
<br/> <br/>$\mathrm{P}(\mathrm{A})=\mathrm{P}\left(\mathrm{E}_{1}\right) \mathrm{P}\left(\mathrm{A} / \mathrm{E}_{1}\right)+\mathrm{P}\left(\mathrm{E}_{2}\right) \mathrm{P}\left(\mathrm{A} / \mathrm{E}_{2}\right)$
<br/> <br/>$\Rightarrow \frac{31}{42}=\frac{n}{2 n+1} \times 1+\frac{n+1}{2 n+1} \times \frac{1}{2}$
<br/> <br/>$\frac{31}{42}=\frac{n}{2 n+1}+\frac{n+1}{2(2 n+1)}$
<br/> <br/>$\Rightarrow \frac{31}{42}=\frac{3 n+1}{2(2 n+1)}$
<br/> <br/>$\Rightarrow \frac{31}{21}=\frac{3 n+1}{2 n+1}$
<br/> <br/>$n=10$</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch1_P1.db
title:
a-bag-contains-3-red-and-3-white-balls-two-balls-are-drawn-one-by-one-the-probability-that-they-are-of-different-colours-is

slug:
a-bag-contains-3-red-and-3-white-balls-two-balls-are-drawn-one-by-one-the-probability-that-they-are-of-different-colours-is-16715

question:
<div class="question">A bag contains 3 red and 3 white balls. Two balls are drawn one by one. The probability that they are of different colours is.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3 / 10$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 / 5$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$3 / 5$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3 / 5$</span> </div>

answer:
<div class="solution">Let $\mathrm{A} \equiv$ event that drawn ball is red $\mathrm{B} \equiv$ event that drawn ball is white Then $\mathrm{AB}$ and $\mathrm{BA}$ are two disjoint cases of the given event.
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\therefore P(A B+B A)=P(A B)+P(B A) \\
<br/> <br/>=P(A) \quad P\left(\frac{B}{A}\right)+P(B) \quad P\left(\frac{A}{B}\right)
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>$=\frac{3}{6} \cdot \frac{3}{5}+\frac{3}{6} \cdot \frac{3}{5}=\frac{3}{5}$</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P1.db
title:
a-bag-contains-5-brown-and-4-white-socks-a-man-pulls-out-2-socks-find-the-probability-that-they-are-of-the-same-colour

slug:
a-bag-contains-5-brown-and-4-white-socks-a-man-pulls-out-2-socks-find-the-probability-that-they-are-of-the-same-colour-13252

question:
<div class="question">A bag contains 5 brown and 4 white socks. $A$ man pulls out 2 socks. Find the probability that they are of the same colour.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{4}{9}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2}{9}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{5}{9}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{7}{9}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{4}{9}$</span> </div>

answer:
<div class="solution">Let $A \equiv$ event of two socks being brown. $\mathrm{B} \equiv$ event of two socks being white.
<br/> <br/>$$
<br/> <br/>\text { Then } \begin{aligned}
<br/> <br/>&amp; P(A)=\frac{{ }^{5} C_{2}}{{ }^{9} C_{2}}=\frac{5.4}{9.8}=\frac{5}{18}, \mathrm{P}(\mathrm{B}) \\
<br/> <br/>&amp;=\frac{{ }^{4} \mathrm{C}_{2}}{{ }^{9} \mathrm{C}_{2}}=\frac{4.3}{9.8}=\frac{3}{18}
<br/> <br/>\end{aligned}
<br/> <br/>$$
<br/> <br/>Now, since $\mathrm{A}$ and $\mathrm{B}$ are mutually exclusive events, so required probability
<br/> <br/>$$
<br/> <br/>=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})=\frac{5}{18}+\frac{3}{18}=\frac{4}{9}
<br/> <br/>$$</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch1_P1.db
title:
a-bag-contains-n-1-coins-it-is-known-that-one-of-these-coins-shows-heads-on-both-sides-whereas-the-other-coins-are-fair-one-coin-is-selected-at-random

slug:
a-bag-contains-n-1-coins-it-is-known-that-one-of-these-coins-shows-heads-on-both-sides-whereas-the-other-coins-are-fair-one-coin-is-selected-at-random-21601

question:
<div class="question">A bag contains $n+1$ coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is $\frac{7}{12},$ then the value of $n$ is.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">4</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">5</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

answer:
<div class="solution">Let $E_{1}$ denote the event "a coin with head on both sides is selected" and $\mathrm{E}_{2}$ denotes the event " a fair coin is selected". Let $A$ be
<br/> <br/>the event " he toss, results in heads".
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\therefore \mathrm{P}\left(\mathrm{E}_{1}\right)=\frac{1}{n+1}, \mathrm{P}\left(\mathrm{E}_{2}\right)=\frac{n}{n+1} \text { and } \\
<br/> <br/>\mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{E}_{1}}\right)=1, \mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{E}_{2}}\right)=\frac{1}{2} \\
<br/> <br/>\therefore \mathrm{P}(\mathrm{A})=\mathrm{P}\left(\mathrm{E}_{1}\right) \mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{E}_{1}}\right)+\mathrm{P}\left(\mathrm{E}_{2}\right) \mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{E}_{2}}\right) \\
<br/> <br/>\Rightarrow \frac{7}{12}=\frac{1}{n+1} \times 1+\frac{n}{n+1} \times \frac{1}{2} \\
<br/> <br/>\Rightarrow 14 n+14=24+12 n \Rightarrow n=5
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Physics', 'Motion In One Dimension', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P1.db
title:
a-ball-is-dropped-vertically-from-a-height-d-above-the-ground-it-hits-the-ground-and-bounces-up-vertically-to-a-height-d-2-neglecting-subsequent-motio-1

slug:
a-ball-is-dropped-vertically-from-a-height-d-above-the-ground-it-hits-the-ground-and-bounces-up-vertically-to-a-height-d-2-neglecting-subsequent-motio-1-82601

question:
<div class="question">A ball is dropped vertically from a height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> above the ground. It hits the ground and bounces up vertically to a height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>/</mo><mn>2</mn><mo>.</mo></math> Neglecting subsequent motion and air resistance, its velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> varies with height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> above the ground as</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/c9f34755-a0da-4eb7-88b7-7d64123d4824-image.png" style="width: 210px; height: 208px;"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/d7fd39e2-dd4c-41fd-acf8-efc69b8c9adf-image.png" style="width: 210px; height: 216px;"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/a16d3a52-2ec5-4b81-af3b-f71233f03b6e-image.png" style="width: 210px; height: 219px;"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/cf90d266-7e93-4f3c-acb2-0bf1599aaab5-image.png" style="width: 210px; height: 208px;"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/c9f34755-a0da-4eb7-88b7-7d64123d4824-image.png" style="width: 210px; height: 208px;"/></span> </div>

answer:
<div class="solution"><p>For the uniformly accelerated/decelcrated motion,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><msup><mi>u</mi><mn>2</mn></msup><mo>±</mo><mn>2</mn><mi>g</mi><mi>h</mi></math></p><p>So. from this equation. we can say <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>-</mo><mi>h</mi></math> paragraph is parabola.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/9a271acb-9ff1-4c78-bc96-8aba42a9ec7d-image.png" style="width: 220px; height: 218px;"/></p><p>Initially, velocity is downwards <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>-</mo><mi>v</mi><mi>e</mi><mo>)</mo></math> after collision, it reverses the direction with smaller magnitude and velocity is upwards <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>-</mo><mi>v</mi><mi>e</mi><mo>)</mo></math>.</p><p>So. graph (a) satisfies these conditions.</p><p>Also, When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>h</mi><mo>=</mo><mi>d</mi></math> Velocity increases downwards <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">U</mi><mo>→</mo><mi mathvariant="normal">A</mi><mo>)</mo></math></p><p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>-</mo><mn>1</mn></math> velocity reverses its direction <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>A</mi><mo>'</mo></msup><mo>→</mo><mi>B</mi></mrow></mfenced></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P1.db
title:
a-ball-of-mass-02-kg-is-thrown-vertically-upwards-by-applying-a-force-by-hand-if-the-hand-moves-02-m-while-applying-the-force-and-the-ball-goes-upto-2

slug:
a-ball-of-mass-02-kg-is-thrown-vertically-upwards-by-applying-a-force-by-hand-if-the-hand-moves-02-m-while-applying-the-force-and-the-ball-goes-upto-2-44834

question:
<div class="question">A ball of mass $0.2 \mathrm{~kg}$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2 \mathrm{~m}$ while applying the force and the ball goes upto $2 \mathrm{~m}$ height further, find the magnitude of the force. (Consider $\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4 \mathrm{~N}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$16 \mathrm{~N}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$20 \mathrm{~N}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$22 \mathrm{~N}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$22 \mathrm{~N}$</span> </div>

answer:
<div class="solution">Let the velocity of the ball just when it leaves the hand is $u$ then applying,
<br/> <br/>$\begin{array}{l}
<br/> <br/>v^{2}-u^{2}=2 a \text { for upward journey } \\
<br/> <br/>\Rightarrow-u^{2}=2(-10) \times 2 \\
<br/> <br/>\Rightarrow u^{2}=40
<br/> <br/>\end{array}$
<br/> <br/>Again applying $v^{2}-u^{2}=2 a s$ for the upward journey of the ball, when the ball is in the hands of the thrower,
<br/> <br/>$\begin{array}{l}
<br/> <br/>v^{2}-u^{2}=2 a s \\
<br/> <br/>\Rightarrow 40-0=2(a) 0.2 \\
<br/> <br/>\Rightarrow a=100 \mathrm{~m} / \mathrm{s}^{2} \\
<br/> <br/>\therefore \mathrm{F}=m a=0.2 \times 100=20 \mathrm{~N} \\
<br/> <br/>\Rightarrow \mathrm{N}-m g=20 \\
<br/> <br/>\Rightarrow \mathrm{N}=20+2=22 \mathrm{~N}
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2013']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch1_P1.db
title:
a-ball-whose-density-is-04-1-0-3-kg-m-3-falls-into-water-from-a-height-of-9-cm-to-what-depth-does-the-ball-sink

slug:
a-ball-whose-density-is-04-1-0-3-kg-m-3-falls-into-water-from-a-height-of-9-cm-to-what-depth-does-the-ball-sink-19247

question:
<div class="question">$\quad$ A ball whose density is $0.4 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ falls into water from a height of $9 \mathrm{~cm}$. To what depth does the ball sink?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \mathrm{~cm}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$6 \mathrm{~cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4.5 \mathrm{~cm}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2.25 \mathrm{~cm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$6 \mathrm{~cm}$</span> </div>


tags: ['Physics', 'Kinetic Theory of Gases', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
title:
a-balloon-is-filled-at-27-c-and-1-atm-pressure-by-500-m-3-he-at-3-c-and-0-5-atm-pressure-the-volume-of-he-will-be

slug:
a-balloon-is-filled-at-27-c-and-1-atm-pressure-by-500-m-3-he-at-3-c-and-0-5-atm-pressure-the-volume-of-he-will-be-35905

question:
<div class="question">A balloon is filled at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo> </mo><mo>°</mo><mi mathvariant="normal">C</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi>atm</mi></math> pressure by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>He</mi></math>. At <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo> </mo><mo>°</mo><mi mathvariant="normal">C</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>atm</mi></math> pressure, the volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>He</mi></math> will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>700</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>900</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>900</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math></span> </div>

answer:
<div class="solution"><p>We have, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msub><mi>P</mi><mn>1</mn></msub><msub><mi>V</mi><mn>1</mn></msub></mrow><msub><mi>T</mi><mn>1</mn></msub></mfrac><mo>=</mo><mfrac><mrow><msub><mi>P</mi><mn>2</mn></msub><msub><mi>V</mi><mn>2</mn></msub></mrow><msub><mi>T</mi><mn>2</mn></msub></mfrac></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><msub><mi>P</mi><mn>1</mn></msub><msub><mi>V</mi><mn>1</mn></msub><msub><mi>T</mi><mn>2</mn></msub></mrow><mrow><msub><mi>P</mi><mn>2</mn></msub><msub><mi>T</mi><mn>1</mn></msub></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>1</mn><mo>×</mo><mn>500</mn><mo>×</mo><mfenced><mrow><mn>273</mn><mo>-</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mfenced><mrow><mn>273</mn><mo>+</mo><mn>27</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>×</mo><mn>500</mn><mo>×</mo><mn>270</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>300</mn></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mn>2</mn></msub><mo>=</mo><mn>900</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math></p></div>


tags: ['Physics', 'Motion In One Dimension', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P1.db
title:
a-balloon-is-rising-vertically-up-with-a-velocity-of-29-ms-1-a-stone-is-dropped-from-it-and-it-reaches-the-ground-in-10-seconds-the-height-of-the-ball

slug:
a-balloon-is-rising-vertically-up-with-a-velocity-of-29-ms-1-a-stone-is-dropped-from-it-and-it-reaches-the-ground-in-10-seconds-the-height-of-the-ball-12306

question:
<div class="question">A balloon is rising vertically up with a velocity of $29 \mathrm{~ms}^{-1}$. A stone is dropped from it and it reaches the ground in 10 seconds. The height of the balloon when the stone was dropped from it, was $\left(\mathrm{g}=9.8 \mathrm{~ms}^{-2}\right)$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$100 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$200 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$400 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$150 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$200 \mathrm{~m}$</span> </div>

answer:
<div class="solution">For stone to be dropped from rising balloon of velocity $29 \mathrm{~m} / \mathrm{s}, \mathrm{u}=-29 \mathrm{~m} / \mathrm{s}, \mathrm{t}=10 \mathrm{sec} .$
<br/> <br/>$\begin{array}{l}
<br/> <br/>\therefore \mathrm{h}=-29 \times 10+\frac{1}{2} \times 9.8 \times 100 \\
<br/> <br/>=-290+490=200 \mathrm{~m} .
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Ray Optics', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P1.db
title:
a-biconvex-lens-has-a-radius-of-curvature-of-magnitude-20-cm-which-one-of-the-following-options-best-describe-the-image-formed-of-an-object-of-height-

slug:
a-biconvex-lens-has-a-radius-of-curvature-of-magnitude-20-cm-which-one-of-the-following-options-best-describe-the-image-formed-of-an-object-of-height-87815

question:
<div class="question">A biconvex lens has a radius of curvature of magnitude $20 \mathrm{~cm}$. Which one of the following options best describe the image formed of an object of height $2 \mathrm{~cm}$ placed $30 \mathrm{~cm}$ from the lens?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Virtual, upright, height $=1 \mathrm{~cm}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Virtual, upright, height $=0.5 \mathrm{~cm}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Real, inverted, height $=4 \mathrm{~cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Real, inverted, height $=1 \mathrm{~cm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Real, inverted, height $=4 \mathrm{~cm}$</span> </div>

answer:
<div class="solution">In the branch containing \(L\) and \(R_{2}\)
<br/> <br/>\(\begin{aligned} &amp;\mathrm{i}=\frac{\mathrm{E}}{\mathrm{R}_{2}}\left(1-\mathrm{e}^{-\frac{\mathrm{R}_{2} \mathrm{t}}{\mathrm{L}}}\right) \\ &amp;\frac{\mathrm{di}}{\mathrm{dt}}=\frac{\mathrm{E}}{\mathrm{R}_{2}} \mathrm{e}^{-\frac{\mathrm{R}_{2} \mathrm{t}}{\mathrm{L}}} \cdot \frac{\mathrm{R}_{2}}{\mathrm{~L}}=\frac{\mathrm{E}}{\mathrm{L}} \mathrm{e}^{-\frac{\mathrm{R}_{2} \mathrm{t}}{\mathrm{L}}} \\ &amp;\therefore \mathrm{V}_{\mathrm{L}}=\mathrm{L} \frac{\mathrm{di}}{\mathrm{dt}}=\mathrm{Ee}^{-\frac{\mathrm{R}_{2} \mathrm{t}}{\mathrm{L}}} \\ &amp;=12 \mathrm{e}^{-\frac{2 \mathrm{t}}{400 \times 10^{-3}}}=12 \mathrm{e}^{-5 \mathrm{t}} \mathrm{V} \end{aligned}\)</div>


tags: ['Physics', 'Kinetic Theory of Gases', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch1_P1.db
title:
a-bicycle-tyre-is-filled-with-air-having-pressure-of-270-kpa-at-2-7-c-the-approximate-pressure-of-the-air-in-the-tyre-when-the-temperature-increases-t

slug:
a-bicycle-tyre-is-filled-with-air-having-pressure-of-270-kpa-at-2-7-c-the-approximate-pressure-of-the-air-in-the-tyre-when-the-temperature-increases-t-42897

question:
<div class="question">A bicycle tyre is filled with air having pressure of $270 \mathrm{kPa}$ at $27^{\circ} \mathrm{C}$. The approximate pressure of the air in the tyre when the temperature increases to $36^{\circ} \mathrm{C}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$270 \mathrm{kPa}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$262 \mathrm{KPa}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$278 \mathrm{kPa}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$360 \mathrm{kPa}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$278 \mathrm{kPa}$</span> </div>

answer:
<div class="solution">From the ideal gas equation $\mathrm{PV}=\mathrm{nRT}$ Here, volume is constant $\therefore \frac{\mathrm{P}_1}{\mathrm{~T}_1}=\frac{\mathrm{P}_2}{\mathrm{~T}_2}$<br/>Here, $T_1=27+273=300 \mathrm{~K}$<br/>$P_1=270 \mathrm{kPa}$<br/>$\mathrm{T}_2=36+273=309 \mathrm{~K}$<br/>$\Rightarrow P_2=\frac{P_1}{T_1} \times T_2=\frac{270 \times(309)}{300}=278 \mathrm{kPa}$</div>


tags: ['Mathematics', 'Functions', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch1_P1.db
title:
a-black-die-and-a-white-die-are-rolled-find-the-probability-that-the-number-shown-by-the-black-die-will-be-more-than-twice-that-shown-by-the-white-die

slug:
a-black-die-and-a-white-die-are-rolled-find-the-probability-that-the-number-shown-by-the-black-die-will-be-more-than-twice-that-shown-by-the-white-die-45511

question:
<div class="question">A black die and a white die are rolled. Find the probability that the number shown by the black die will be more than twice that shown by the white die.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(1 / 8\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(1 / 6\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(1 / 3\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(1 / 4\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(1 / 6\)</span> </div>

answer:
<div class="solution">The number of favourable cases are shown below:<br/>\(\begin{array}{cl}\text { Number on white die } &amp; \text { Number on black die } \\ 1 &amp; 3 \\ 1 &amp; 4 \\ 1 &amp; 5 \\ 1 &amp; 6 \\ 2 &amp; 5 \\ 2 &amp; 6\end{array}\)<br/>There are 6 favourable cases in which the number on black die is more than twice the number on the white die.<br/>\(\begin{aligned}<br/>&amp; \therefore \mathrm{m}=6 \\<br/>&amp; \mathrm{n}=\text { Total number of cases }=6 \times 6<br/>\end{aligned}\)<br/>( \(\therefore\) with each die there are six possibilities)<br/>\(\therefore\) Probability \(\mathrm{p}=\frac{\mathrm{m}}{\mathrm{n}}=\frac{6}{6 \times 6}=\frac{1}{6}\)</div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
title:
a-block-a-of-mass-100-kg-rests-on-another-block-b-of-mass-200-kg-and-is-tied-to-a-wall-as-shown-in-the-figure-the-coefficient-of-friction-between-a-an

slug:
a-block-a-of-mass-100-kg-rests-on-another-block-b-of-mass-200-kg-and-is-tied-to-a-wall-as-shown-in-the-figure-the-coefficient-of-friction-between-a-an-78769

question:
<div class="question"><p>A block <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mi>kg</mi></math> rests on another block <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mo> </mo><mi>kg</mi></math> and is tied to a wall as shown in the figure. The coefficient of friction between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>2</mn></math> and that between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> and ground is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>3</mn></math>. The minimum force required to move the block <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>g</mi><mo>=</mo><mn>10</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfenced></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/20b64890-e2fb-4605-8f23-17f02bacd887-image.png" style="width: 300px; height: 129px;"/></p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>900</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1100</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>700</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1100</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </div>

answer:
<div class="solution"><p>Friction force between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> and between block <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> and surface <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math> will oppose <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi>F</mi><mo>=</mo><msub><mi>F</mi><mrow><mi>A</mi><mi>B</mi></mrow></msub><mo>+</mo><msub><mi>F</mi><mrow><mi>B</mi><mi>S</mi></mrow></msub><mo>=</mo><msub><mi>μ</mi><mrow><mi>A</mi><mi>B</mi></mrow></msub><msub><mi>M</mi><mi>A</mi></msub><mi>g</mi><mo>+</mo><msub><mi>μ</mi><mrow><mi>B</mi><mi>S</mi></mrow></msub><mfenced><mrow><msub><mi>m</mi><mi>A</mi></msub><mo>+</mo><msub><mi>m</mi><mi>B</mi></msub></mrow></mfenced><mi>g</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mo>×</mo><mn>100</mn><mo>×</mo><mn>10</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>3</mn><mfenced><mrow><mn>100</mn><mo>+</mo><mn>200</mn></mrow></mfenced><mo>×</mo><mn>10</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>200</mn><mo>+</mo><mn>900</mn><mo>=</mo><mn>1100</mn><mo> </mo><mi mathvariant="normal">N</mi></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P1.db
title:
a-block-of-mass-m-is-placed-on-a-smooth-inclined-wedge-a-bc-of-inclination-as-shown-in-the-figure-the-wedge-is-given-an-acceleration-a-towards-the-rig

slug:
a-block-of-mass-m-is-placed-on-a-smooth-inclined-wedge-a-bc-of-inclination-as-shown-in-the-figure-the-wedge-is-given-an-acceleration-a-towards-the-rig-90068

question:
<div class="question">A block of mass m is placed on a smooth inclined wedge $A B C$ of inclination $\theta$ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and $\theta$ for the block to remain stationary on the wedge is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/6elWAXz6q9osdRlGR5hP02iRBVuwHR0J8DkFfiRalJA.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$a=\frac{g}{\operatorname{cosec} \theta}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$a=\frac{g}{\sin \theta}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$a=g \tan \theta$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$a=g \cos \theta$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$a=g \tan \theta$</span> </div>

answer:
<div class="solution">Let the mass of block is m. It will remains stationary if forces acting on it are in equilibrium. i.e., $m a \cos \theta=m g \sin \theta$
<br/> <br/>$\Rightarrow a=g \tan \theta$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/6Kt7aR7rSEsAgzZdB-12ihl9_xlN6SnNnJoueun6tjg.original.fullsize.png"/><br/> <br/> <br/>Here $\mathrm{ma}=$ Pseudo force on block,
<br/> <br/>$\mathrm{mg}=$ weight</div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2009']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch1_P1.db
title:
a-block-of-mass-m-is-pulled-along-a-horizontal-frictionless-surface-by-a-rope-of-mass-m-2-if-a-force-2-mg-is-applied-at-one-end-of-the-rope-the-force-

slug:
a-block-of-mass-m-is-pulled-along-a-horizontal-frictionless-surface-by-a-rope-of-mass-m-2-if-a-force-2-mg-is-applied-at-one-end-of-the-rope-the-force-13325

question:
<div class="question">A block of mass $\mathrm{M}$ is pulled along a horizontal frictionless surface by a rope of mass $\mathrm{M} / 2$. If a force $2 \mathrm{Mg}$ is applied at one end of the rope, the force which the rope exerts on the block is -</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \mathrm{Mg} / 3$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \mathrm{Mg}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$4 \mathrm{Mg} / 3$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">zero</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 \mathrm{Mg} / 3$</span> </div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P1.db
title:
a-block-of-wood-floats-in-water-with-4-5-th-of-its-volume-submerged-if-the-same-block-just-floate-in-a-liquid-the-density-of-liquid-in-kg-m-3-is

slug:
a-block-of-wood-floats-in-water-with-4-5-th-of-its-volume-submerged-if-the-same-block-just-floate-in-a-liquid-the-density-of-liquid-in-kg-m-3-is-14758

question:
<div class="question">A block of wood floats in water with <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>4</mn><mo>/</mo><mn>5</mn><msup><mo>)</mo><mi>th</mi></msup></math> of its volume submerged. If the same block just floate in a liquid, the density of liquid in <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfenced></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1250</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>800</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>800</mn></math></span> </div>

answer:
<div class="solution"><p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> be the volume of the block. When block floats in water, then <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow><mi>block</mi><mo> </mo></mrow></msub><mi>g</mi><mo>=</mo><mfenced><mrow><mfrac><mn>4</mn><mn>5</mn></mfrac><mi>v</mi></mrow></mfenced><msub><mi>ρ</mi><mrow><mi>water</mi><mo> </mo></mrow></msub><mi>g</mi></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mi>block</mi></msub><mo>=</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><msub><mi>ρ</mi><mrow><mi>water</mi><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo></mrow></msub><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi mathvariant="normal">i</mi></mfenced></math></p><p>When block floats in liquid.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><msub><mi>ρ</mi><mrow><mi>block</mi><mo> </mo></mrow></msub><mi>g</mi><mo>=</mo><mi>V</mi><msub><mi>ρ</mi><mi>liquid</mi></msub><mi>g</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ρ</mi><mrow><mi>block</mi><mo> </mo></mrow></msub><mo>=</mo><msub><mi>ρ</mi><mrow><mi>liquid</mi><mo> </mo></mrow></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ρ</mi><mrow><mi>liquid</mi><mo> </mo></mrow></msub><mo>=</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><msub><mi>ρ</mi><mrow><mi>water</mi><mo> </mo></mrow></msub></math> [from Eq. (i)]</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>800</mn><mo> </mo><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P1.db
title:
a-bob-is-hanging-over-a-pulley-inside-a-car-through-a-string-the-second-end-of-the-string-is-in-the-hand-of-a-person-standing-in-the-car-the-car-is-mo

slug:
a-bob-is-hanging-over-a-pulley-inside-a-car-through-a-string-the-second-end-of-the-string-is-in-the-hand-of-a-person-standing-in-the-car-the-car-is-mo-21453

question:
<div class="question">A bob is hanging over a pulley inside a car through, a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' directed horizontallyas shown in figure. Other end of the string is pulled with constant acceleration 'a' vertically. The tension in the string is equal to -
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/MeCzqZkN_4t-0bPL-U9GAfikCf7uFvQ2jL2VZc9tzKw.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$m \sqrt{g^{2}+a^{2}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$m \sqrt{g^{2}+a^{2}}-m a$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{m} \sqrt{\mathrm{g}^{2}+\mathrm{a}^{2}}+\mathrm{ma}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{m}(\mathrm{g}+\mathrm{a})$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{m} \sqrt{\mathrm{g}^{2}+\mathrm{a}^{2}}+\mathrm{ma}$</span> </div>

answer:
<div class="solution">Applying Newton's law
<br/> <br/>along string
<br/> <br/>$$
<br/> <br/>\Rightarrow \mathrm{T}-\mathrm{m} \sqrt{\mathrm{g}^{2}+\mathrm{a}^{2}}=\mathrm{ma}
<br/> <br/>$$
<br/> <br/>or $\mathrm{T}=\mathrm{m} \sqrt{\mathrm{g}^{2}+\mathrm{a}^{2}}+\mathrm{ma}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/LkCzNOWXg3KqhyEpoBFRL0Q4wHXBJ8DHCj7AxaIoNk8.original.fullsize.png"/></div>


tags: ['Physics', 'Work Power Energy', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P1.db
title:
a-body-is-moving-unidirectionally-under-the-influence-of-a-source-of-constant-power-the-square-of-its-displacement-in-time-t-is-proportional-to

slug:
a-body-is-moving-unidirectionally-under-the-influence-of-a-source-of-constant-power-the-square-of-its-displacement-in-time-t-is-proportional-to-70935

question:
<div class="question">A body is moving unidirectionally under the influence of a source of constant power. The square of its displacement in time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is proportional to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>t</mi><mn>3</mn></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>t</mi><mn>2</mn></msup></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>t</mi></msqrt></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>t</mi><mn>3</mn></msup></math></span> </div>

answer:
<div class="solution"><p>By work-energy theorem,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mi>P</mi><mo>×</mo><mi>t</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><mn>2</mn><mfrac><mrow><mi>P</mi><mi>t</mi></mrow><mi>m</mi></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msup><mfenced><mfrac><mrow><mn>2</mn><mi>P</mi><mi>t</mi></mrow><mi>m</mi></mfrac></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>d</mi><mi>s</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msup><mfenced><mfrac><mrow><mn>2</mn><mi>P</mi><mi>t</mi></mrow><mi>m</mi></mfrac></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo><mi>d</mi><mi>s</mi><mo>=</mo><mo>∫</mo><msup><mfenced><mfrac><mrow><mn>2</mn><mi>P</mi><mi>t</mi></mrow><mi>m</mi></mfrac></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mi>d</mi><mi>t</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msup><mfenced><mfrac><mrow><mn>2</mn><mi>P</mi></mrow><mi>m</mi></mfrac></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>·</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><msup><mi>t</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></math></p><p>i.e. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>∝</mo><msup><mi>t</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>s</mi><mn>2</mn></msup><mo>∝</mo><msup><mi>t</mi><mn>3</mn></msup></math></p></div>


tags: ['Physics', 'Motion In Two Dimensions', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P1.db
title:
a-body-is-projected-making-an-acute-angle-with-the-horizontal-if-angle-between-velocity-v-and-acceleration-g-is-then

slug:
a-body-is-projected-making-an-acute-angle-with-the-horizontal-if-angle-between-velocity-v-and-acceleration-g-is-then-89835

question:
<div class="question">A body is projected, making an acute angle with the horizontal. If angle between velocity $\vec{v}$ and acceleration $\overrightarrow{\mathrm{g}}$ is $\theta,$ then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\theta=90^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\quad \theta=0^{\circ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$90^{\circ}&lt;\theta&lt;0^{\circ}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$0^{\circ}&lt;\theta&lt;180^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0^{\circ}&lt;\theta&lt;180^{\circ}$</span> </div>

answer:
<div class="solution">Here velocity is acting upwards when projectile is going upwards and acceleration is downwards. The angle $\theta$ between $\overrightarrow{\mathrm{v}}$ and $\overrightarrow{\text { a }}$ is more than $0^{\circ}$ and less than $180^{\circ}$</div>


tags: ['Physics', 'Motion In One Dimension', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch1_P1.db
title:
a-body-is-thrown-vertically-upwards-from-a-the-top-of-the-tower-reaches-the-ground-in-time-t-1-if-it-is-thrown-vertically-downwards-from-a-with-the-sa

slug:
a-body-is-thrown-vertically-upwards-from-a-the-top-of-the-tower-reaches-the-ground-in-time-t-1-if-it-is-thrown-vertically-downwards-from-a-with-the-sa-25864

question:
<div class="question">A body is thrown vertically upwards from A, the top of the tower, reaches the ground in time $t_{1}$. If it is thrown vertically downwards from A with the same speed, it reaches the ground in time $\mathrm{t}_{2}$. If it is allowed to fall freely from $\mathrm{A},$ then the time it takes to reach the ground is given by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{t}=\frac{\mathrm{t}_{1}+\mathrm{t}_{2}}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{t}=\frac{\mathrm{t}_{1}-\mathrm{t}_{2}}{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\quad \mathrm{t}=\sqrt{\mathrm{t}_{1} \mathrm{t}_{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{t}=\sqrt{\frac{\mathrm{t}_{1}}{\mathrm{t}_{2}}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad \mathrm{t}=\sqrt{\mathrm{t}_{1} \mathrm{t}_{2}}$</span> </div>

answer:
<div class="solution">Let the body is projected vertically upwards from A with a speed $u_{0}$ Using equation, $\mathrm{s}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^{2}$
<br/> <br/>For case $(1)-\mathrm{h}=\mathrm{u}_{0} \mathrm{t}_{1}-\frac{1}{2} \mathrm{gt}_{1}^{2} \quad \ldots(1)$
<br/> <br/>For case (2) $-\mathrm{h}=\mathrm{u}_{0} \mathrm{t}_{2}-\frac{1}{2} \mathrm{gt}_{1}^{2}$
<br/> <br/>Subtracting eq (2) from (1), we get
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>0=\mathrm{u}_{0}\left(\mathrm{t}_{2}+\mathrm{t}_{1}\right)+\frac{1}{2} \mathrm{~g}\left(\mathrm{t}_{2}^{2}-\mathrm{t}_{1}^{2}\right) \\
<br/> <br/>\Rightarrow \mathrm{u}_{0}=\frac{1}{2} \mathrm{~g}\left(\mathrm{t}_{1}-\mathrm{t}_{2}\right)
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Putting the value of $\mathrm{u}_{0}$ in eq (2), we get
<br/> <br/>$$
<br/> <br/>-\mathrm{h}=-\left(\frac{1}{2}\right) \mathrm{g}\left(\mathrm{t}_{1}-\mathrm{t}_{2}\right) \mathrm{t}_{2}-\left(\frac{1}{2}\right) \mathrm{gt}_{2}^{2}
<br/> <br/>$$
<br/> <br/>$$
<br/> <br/>\Rightarrow \mathrm{h}=\frac{1}{2} \mathrm{~g}\left(\mathrm{t}_{1} \mathrm{t}_{2}\right)
<br/> <br/>$$
<br/> <br/>For case $3, \mathrm{u}_{0}=0, \mathrm{t}=?$
<br/> <br/>$$
<br/> <br/>-\mathrm{h}=0 \times \mathrm{t}-\left(\frac{1}{2}\right) \mathrm{gt}^{2}
<br/> <br/>$$
<br/> <br/>$\mathrm{h}=\left(\frac{1}{2}\right) \mathrm{gt}^{2}$
<br/> <br/>Comparing eq. (4) and $(5),$ we get
<br/> <br/>$$
<br/> <br/>\frac{1}{2} \mathrm{gt}^{2}=\frac{1}{2} \mathrm{gt}_{1} \mathrm{t}_{2} \quad \therefore \mathrm{t}=\sqrt{\mathrm{t}_{1} \mathrm{t}_{2}}
<br/> <br/>$$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
a-body-of-density-is-dropped-from-rest-at-a-height-h-into-a-lake-of-density-where-neglecting-all-dissipative-forces-calculate-the-maximum-depth-to-whi

slug:
a-body-of-density-is-dropped-from-rest-at-a-height-h-into-a-lake-of-density-where-neglecting-all-dissipative-forces-calculate-the-maximum-depth-to-whi-25576

question:
<div class="question">A body of density $\rho^{\prime}$ is dropped from rest at a height h into a lake of density $\rho$ where $\rho&gt;\rho^{\prime}$ neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{h}}{\rho-\rho^{\prime}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\mathrm{h} \rho^{\prime}}{\rho}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{h} \rho^{\prime}}{\rho-\rho^{\prime}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{h \rho}{\rho-\rho^{\prime}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{h} \rho^{\prime}}{\rho-\rho^{\prime}}$</span> </div>

answer:
<div class="solution">The effective acceleration of the body
<br/> <br/>$\mathrm{g}^{\prime}=\left(1-\frac{\rho}{\rho^{\prime}}\right) \mathrm{g}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/oEm_LCHuM0OzQE1UaLX4fufNHlvQQinJ9ebj1CpNf08.original.fullsize.png"/><br/> <br/> <br/>Now, the depth to which the body sinks
<br/> <br/>$\mathrm{h}^{\prime}=\left(\frac{\mathrm{u}^{2}}{2 \mathrm{~g}^{\prime}}\right)=\frac{2 \mathrm{gh}}{2 \mathrm{~g}^{\prime}}=\frac{\mathrm{gh}}{\mathrm{g}^{\prime}}=\frac{\mathrm{h} \times \rho^{\prime}}{\rho-\rho^{\prime}}$</div>


tags: ['Physics', 'Thermal Properties of Matter', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P1.db
title:
a-body-of-length-1-m-having-crosssectional-area-075-m-2-has-heat-flow-through-it-at-the-rate-of-6000-joulesec-then-find-the-temperature-difference-if-

slug:
a-body-of-length-1-m-having-crosssectional-area-075-m-2-has-heat-flow-through-it-at-the-rate-of-6000-joulesec-then-find-the-temperature-difference-if-55294

question:
<div class="question">A body of length $1 \mathrm{~m}$ having cross-sectional area $0.75 \mathrm{~m}^{2}$ has heat flow through it at the rate of 6000 Joule/sec. Then find the temperature difference if $\mathrm{K}=200 \mathrm{Jm}^{-1} \mathrm{~K}^{-1}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$20^{\circ} \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$40^{\circ} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$80^{\circ} \mathrm{C}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$100^{\circ} \mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$40^{\circ} \mathrm{C}$</span> </div>

answer:
<div class="solution">$\frac{Q}{t}=\frac{\operatorname{KA} \Delta \theta}{\ell} \Rightarrow 6000=\frac{200 \times 0.75 \times \Delta \theta}{1}$<br/>$\therefore \Delta \theta=\frac{6000 \times 1}{200 \times 0.75}=40^{\circ} \mathrm{C}$</div>


tags: ['Physics', 'Oscillations', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
title:
a-body-of-mass-1-kg-is-executing-simple-harmonic-motion-its-displacement-y-cm-at-t-seconds-is-given-by-y-6-sin-100-t-4-its-maximum-kinetic-energy-is

slug:
a-body-of-mass-1-kg-is-executing-simple-harmonic-motion-its-displacement-y-cm-at-t-seconds-is-given-by-y-6-sin-100-t-4-its-maximum-kinetic-energy-is-43169

question:
<div class="question"><p>A body of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi>kg</mi></math> is executing simple harmonic motion. Its displacement <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mfenced><mi>cm</mi></mfenced></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>6</mn><mi>sin</mi><mfenced><mrow><mn>100</mn><mi>t</mi><mo>+</mo><mfrac><mi>π</mi><mn>4</mn></mfrac></mrow></mfenced></math>. Its maximum kinetic energy is</p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo> </mo><mi mathvariant="normal">J</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mi mathvariant="normal">J</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo> </mo><mi mathvariant="normal">J</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn><mo> </mo><mi mathvariant="normal">J</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mi mathvariant="normal">J</mi></math></span> </div>

answer:
<div class="solution"><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>6</mn><mo> </mo><mi>cm</mi><mo>=</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">ω</mi><mo>=</mo><mn>100</mn><mo> </mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mi mathvariant="normal">m</mi><mo>=</mo><mn>1</mn><mo> </mo><mi>kg</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>K</mi><mi>max</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>ω</mi><mn>2</mn></msup><msup><mi>a</mi><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>1</mn><mo>×</mo><msup><mfenced><mn>100</mn></mfenced><mn>2</mn></msup><mo>×</mo><msup><mfenced><mrow><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfenced><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>18</mn><mo> </mo><mi mathvariant="normal">J</mi></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
a-body-of-mass-2-kg-is-placed-on-a-horizontal-surface-having-kinetic-friction-04-and-static-friction-05-if-the-force-applied-on-the-body-is-25-n-then-

slug:
a-body-of-mass-2-kg-is-placed-on-a-horizontal-surface-having-kinetic-friction-04-and-static-friction-05-if-the-force-applied-on-the-body-is-25-n-then-96001

question:
<div class="question">A body of mass $2 \mathrm{~kg}$ is placed on a horizontal surface having kinetic friction 0.4 and static friction $0.5 .$ If the force applied on the body is $2.5 \mathrm{~N},$ then the frictional force acting on the body will be $\left[\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$8 \mathrm{~N}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 \mathrm{~N}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$20 \mathrm{~N}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$2.5 \mathrm{~N}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2.5 \mathrm{~N}$</span> </div>

answer:
<div class="solution">Limiting friction $=0.5 \times 2 \times 10=10 \mathrm{~N}$
<br/> <br/>The applied force is less than force of friction, therefore the force of friction is equal to the applied force.</div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P1.db
title:
a-body-of-mass-m-is-moving-in-a-straight-line-with-momentum-p-starting-at-time-t-0-a-force-f-a-t-acts-in-the-same-direction-on-the-moving-particle-dur

slug:
a-body-of-mass-m-is-moving-in-a-straight-line-with-momentum-p-starting-at-time-t-0-a-force-f-a-t-acts-in-the-same-direction-on-the-moving-particle-dur-86637

question:
<div class="question">A body of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> is moving in a straight line with momentum <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>. Starting at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>, a force <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>a</mi><mi>t</mi></math> acts in the same direction on the moving particle during time interval of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>. So that its momentum changes from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>p</mi></math>. The value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mi>a</mi></mfrac></msqrt></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mi>p</mi><mi>a</mi></mfrac></msqrt></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msqrt><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mi>a</mi></mfrac></msqrt></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mi>a</mi></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mi>a</mi></mfrac></msqrt></math></span> </div>

answer:
<div class="solution"><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>a</mi><mi>t</mi></math></p><p>when, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>, then linear momentum <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>p</mi></math></p><p>when, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>T</mi></math>, then linear momentum <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mi>p</mi></math></p><p>According to Newton's law of motion, applied force, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>p</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>p</mi><mo>=</mo><mi>F</mi><mi>d</mi><mi>t</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>p</mi><mo>=</mo><mi>a</mi><mi>t</mi><mi>d</mi><mi>t</mi></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mi>p</mi><mrow><mn>2</mn><mi>p</mi></mrow></msubsup><mi>d</mi><mi>p</mi><mo>=</mo><mi>a</mi><msubsup><mo>∫</mo><mn>0</mn><mi>T</mi></msubsup><mi>t</mi><mi>d</mi><mi>t</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mi>p</mi><mo>-</mo><mi>p</mi></mrow></mfenced><mo>=</mo><mi>a</mi><mo>·</mo><mfrac><msup><mi>T</mi><mn>2</mn></msup><mn>2</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mi>a</mi></mfrac><mo>=</mo><msup><mi>T</mi><mn>2</mn></msup><mo>⇒</mo><mi>T</mi><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mi>a</mi></mfrac></msqrt></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P1.db
title:
a-body-of-weight-2-kg-is-suspended-as-shown-in-the-figure-the-tension-t-1-in-the-horizontal-string-in-kg-wt-is

slug:
a-body-of-weight-2-kg-is-suspended-as-shown-in-the-figure-the-tension-t-1-in-the-horizontal-string-in-kg-wt-is-74110

question:
<div class="question">A body of weight $2 \mathrm{~kg}$ is suspended as shown in the figure. The tension $\mathrm{T}_{1}$ in the horizontal string (in $\mathrm{kg}$ wt ) is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/M1AX_eSftPIY0bQ28YXsaE8NAl_9yaLTo_jffdjtHu4.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{2}{\sqrt{3}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\sqrt{3}}{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$2 \sqrt{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \sqrt{3}$</span> </div>

answer:
<div class="solution">The tension in the above string can be divided into two components where the component opposite to weight will balance the weight while the component of this tension opposite to \(\mathrm{T}_{1}\) will be equal to \(\mathrm{T}_{1}\).
<br/> <br/>\(\mathrm{T} \sin \theta=2 \mathrm{~kg} \mathrm{wt}\)
<br/> <br/>\(\mathrm{T} \cos \theta=\mathrm{T}_{1}\)
<br/> <br/>The first equation gives
<br/> <br/>\(\mathrm{T}=4 \mathrm{~kg} \mathrm{wt}\)
<br/> <br/>So \(\mathrm{T}_{1}\) will be,
<br/> <br/>\(\mathrm{T}_{1}=2 \sqrt{3} \mathrm{~kg} \mathrm{wt}\)</div>


tags: ['Physics', 'Thermal Properties of Matter', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-bowl-filled-with-very-hot-soup-cools-from-9-8-c-to-8-6-c-in-2-minutes-when-the-room-temperature-is-2-2-c-how-long-it-will-take-to-cool-from-7-5-c-to

slug:
a-bowl-filled-with-very-hot-soup-cools-from-9-8-c-to-8-6-c-in-2-minutes-when-the-room-temperature-is-2-2-c-how-long-it-will-take-to-cool-from-7-5-c-to-60197

question:
<div class="question">A bowl filled with very hot soup cools from $98^{\circ} \mathrm{C}$ to $86^{\circ} \mathrm{C}$ in 2 minutes when the room temperature is $22^{\circ} \mathrm{C}$. How long it will take to cool from $75^{\circ} \mathrm{C}$ to $69^{\circ} \mathrm{C}$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>2 minutes</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>1.4 minutes</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>0.5 minute</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>1 minute</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>1.4 minutes</span> </div>

answer:
<div class="solution">The rate of heat flow is given by<br/>$\begin{aligned}<br/>&amp; \frac{\Delta Q}{\Delta t}=-K\left(T-T_0\right) \Rightarrow \frac{\Delta Q}{\Delta t}=-K\left(T_{a v g}-T_0\right) \\<br/>&amp; \text { Initially } T_{a v g}=\frac{T_1+T_2}{2} \\<br/>&amp; \text { Here, } T_1=98^{\circ} \mathrm{C} \\<br/>&amp; T_2=86^{\circ} \mathrm{C}<br/>\end{aligned}$<br/>$\begin{aligned} &amp; \text { (i) } \frac{\mathrm{ms} \times 12}{2}=-\mathrm{K}\left(\frac{98+86}{2}-22\right) \\ &amp; 6=-\frac{\mathrm{K}}{\mathrm{ms}}\left[\frac{98+86}{2}-22\right] \quad(\because \Delta \mathrm{Q}=\mathrm{ms} \Delta \mathrm{T})\end{aligned}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/m-qxoSp3pUGTs9hNmklcIiM0y5wsfF4lw7tCcyRjGXc.original.fullsize.png"/><br/><br/>Now, cool from $\mathrm{T}_1^{\prime}=75^{\circ} \mathrm{C}$<br/>$\begin{aligned}<br/>&amp; \mathrm{T}_2=69^{\circ} \mathrm{C} \\<br/>&amp; \mathrm{T}_{\mathrm{avg}}=\frac{\mathrm{T}_1^{\prime}+\mathrm{T}_2^{\prime}}{2}=\frac{75+69}{2}<br/>\end{aligned}$<br/>(ii) $\frac{\mathrm{ms} \times 6}{\Delta \mathrm{t}}=-\mathrm{K}\left(\frac{75+69}{2}-22\right)$<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/bQrJV0HZxZIN7yecVk6HwfeL4MYFknI9xPA7NGCSfTw.original.fullsize.png"/><br/><br/>Divide equation (ii) by (i), we have<br/>$\begin{aligned}<br/>&amp; \frac{6}{\Delta t(6)}=\frac{50}{70} \\<br/>&amp; \Delta t=\frac{7}{5}=1.4 \mathrm{~min}<br/>\end{aligned}$</div>


tags: ['Mathematics', 'Permutation Combination', 'BITSAT', 'BITSAT 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">64</span> </div>
source_db: MarksBatch1_P1.db
title:
a-box-contains-two-white-balls-three-black-balls-and-four-red-balls-in-how-many-ways-can-three-balls-be-drawn-from-the-box-if-at-least-one-black-ball-

slug:
a-box-contains-two-white-balls-three-black-balls-and-four-red-balls-in-how-many-ways-can-three-balls-be-drawn-from-the-box-if-at-least-one-black-ball-64031

question:
<div class="question">A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">64</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">129</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">84</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

answer:
<div class="solution">Atleast one black ball can be drawn in the following ways
<br/> <br/>(1) one black and two other colour balls
<br/> <br/>$$
<br/> <br/>={ }^{3} \mathrm{C}_{1} \times{ }^{6} \mathrm{C}_{2}=3 \times 15=45
<br/> <br/>$$
<br/> <br/>(ii) two black and one other colour balls
<br/> <br/>$$
<br/> <br/>={ }^{3} \mathrm{C}_{2} \times{ }^{6} \mathrm{C}_{1}=3 \times 6=18
<br/> <br/>$$
<br/> <br/>(iii) All the three are black $={ }^{3} \mathrm{C}_{3} \times{ }^{6} \mathrm{C}_{0}=1$
<br/> <br/>$\therefore$ Req. no. of ways $=45+18+1=64$</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P1.db
title:
a-boy-is-throwing-stones-at-a-target-the-probability-of-hitting-the-target-at-any-trial-is-2-1-the-probability-of-hitting-the-target-5-th-time-at-the-

slug:
a-boy-is-throwing-stones-at-a-target-the-probability-of-hitting-the-target-at-any-trial-is-2-1-the-probability-of-hitting-the-target-5-th-time-at-the-73318

question:
<div class="question">A boy is throwing stones at a target. The probability of hitting the target at any trial is $\frac{1}{2}$ The probability of hitting the target 5 th time at the 10 th throw is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{5}{2^{10}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{63}{2^{9}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{10}{2^{10}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{63}{2^{9}}$</span> </div>

answer:
<div class="solution">The probability of hitting the target 5 th time at the 10 th throw $=\mathrm{P}($ the probability of hitting the target 4 times in the first 9 throws) $\mathrm{P}($ the probability of hitting the target at the 10 th throw $)=$
<br/>$\left[{ }^{9} \mathrm{C}_{4}\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{5}\right]\left(\frac{1}{2}\right)=\frac{9 !}{4 ! 5 !} \times\left(\frac{1}{2}\right)^{10}=\frac{63}{2^{9}}$</div>


tags: ['Physics', 'Work Power Energy', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
a-boy-pushes-a-toy-box-20-m-along-the-floor-by-means-of-a-force-of-10-n-directed-downward-at-an-angle-of-6-0-to-the-horizontal-the-work-done-by-the-bo

slug:
a-boy-pushes-a-toy-box-20-m-along-the-floor-by-means-of-a-force-of-10-n-directed-downward-at-an-angle-of-6-0-to-the-horizontal-the-work-done-by-the-bo-61126

question:
<div class="question">A boy pushes a toy box $2.0 \mathrm{~m}$ along the floor by means of a force of $10 \mathrm{~N}$ directed downward at an angle of $60^{\circ}$ to the horizontal. The work done by the boy is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$6 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$8 \mathrm{~J}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$10 \mathrm{~J}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$12 \mathrm{~J}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10 \mathrm{~J}$</span> </div>

answer:
<div class="solution">$\mathrm{W}=\mathrm{F} \mathrm{s} \cos \theta=10 \times 2 \cos 60^{\circ}=10 \mathrm{~J}$</div>


tags: ['Physics', 'Capacitance', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-capacitor-of-capacitance-c-is-charged-to-a-potential-v-the-flux-of-the-electric-field-through-a-closed-surface-enclosing-the-positive-plate-of-the-c-1

slug:
a-capacitor-of-capacitance-c-is-charged-to-a-potential-v-the-flux-of-the-electric-field-through-a-closed-surface-enclosing-the-positive-plate-of-the-c-1-75151

question:
<div class="question">A capacitor of capacitance $C$ is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{C V}{2 \varepsilon_0}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2 \mathrm{CV}}{\varepsilon_0}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{CV}}{\varepsilon_0}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Zero</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{CV}}{\varepsilon_0}$</span> </div>

answer:
<div class="solution">From the Gauss's law<br/>$\begin{aligned}<br/>&amp; \phi=\frac{\mathrm{q}_{\text {in }}}{\epsilon_0}=\frac{\mathrm{Q}}{\epsilon_0} \quad \because \mathrm{Q}=\mathrm{CV} \\<br/>&amp; \therefore \phi=\frac{\mathrm{CV}}{\epsilon_0}<br/>\end{aligned}$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch1_P1.db
title:
a-capillary-tube-is-attached-horizontally-to-a-constant-heat-arrangement-if-the-radius-of-the-capillary-tube-is-increased-by-25-then-the-rate-of-flow-

slug:
a-capillary-tube-is-attached-horizontally-to-a-constant-heat-arrangement-if-the-radius-of-the-capillary-tube-is-increased-by-25-then-the-rate-of-flow-17780

question:
<div class="question">A capillary tube is attached horizontally to a constant heat arrangement. If the radius of the capillary tube is increased by $25 \%$, then the rate of flow of liquid will change nearly by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$100 \%$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$112 \%$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$124 \%$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>$144 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$144 \%$</span> </div>

answer:
<div class="solution">Liquid volume coming out of the tube per second
<br/>$$
<br/>\begin{aligned}
<br/>&amp; \quad V=\frac{p \pi r^4}{8 \eta l} \\
<br/>&amp; \Rightarrow \\
<br/>&amp; \Rightarrow \frac{V_2}{V_1}=\left[\frac{r_2}{r_1}\right]^4 \Rightarrow V_2=V_1\left[\frac{125}{100}\right]^4=V_1\left(\frac{5}{4}\right)^4 \\
<br/>&amp; \Rightarrow \\
<br/>&amp; \text { So, now } \frac{\Delta V}{V}=\frac{V_2-V_1}{V_1}=\frac{(244) V_1-V_1}{V_1}=144 \%
<br/>\end{aligned}
<br/>$$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P1.db
title:
a-capillary-tube-of-radius-r-is-immersed-vertically-in-a-liquid-such-that-liquid-rises-in-it-to-height-h-less-than-the-length-of-the-tube-mass-of-liqu

slug:
a-capillary-tube-of-radius-r-is-immersed-vertically-in-a-liquid-such-that-liquid-rises-in-it-to-height-h-less-than-the-length-of-the-tube-mass-of-liqu-66320

question:
<div class="question">A capillary tube of radius $\mathrm{r}$ is immersed vertically in a liquid such that liquid rises in it to height $\mathrm{h}$ (less than the length of the tube). Mass of liquid in the capillary tube is $\mathrm{m}$. If radius of the capillary tube is increased by $50 \%$, then mass of liquid that will rise in the tube, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{2}{3} \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{m}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{3}{2} \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{9}{4} \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3}{2} \mathrm{~m}$</span> </div>

answer:
<div class="solution">$\mathrm{h}=\frac{2 \mathrm{~T} \cos \theta}{\mathrm{r} \rho \mathrm{g}} \Rightarrow \mathrm{h} \propto \frac{1}{\mathrm{r}} \Rightarrow \frac{\mathrm{h}_{2}}{\mathrm{~h}_{1}}=\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{2}{3}$
<br/> <br/>$$
<br/> <br/>\begin{aligned}
<br/> <br/>\left(\because \mathrm{r}_{1}=\mathrm{r}, \quad \mathrm{r}_{2}\right.&amp;=\mathrm{r}+50 \% \text { of } \left.\mathrm{r}=\frac{3}{2} \mathrm{r}\right) \\
<br/> <br/>\text { New mass } \mathrm{m}_{2}=\pi \mathrm{r}_{2}^{2} \mathrm{~h}_{2} \rho &amp;=\pi\left(\frac{3}{2} \mathrm{r}_{1}\right)^{2}\left(\frac{2}{3} \mathrm{~h}_{1}\right) \rho \\
<br/> <br/>&amp;=\frac{3}{2}\left(\pi \mathrm{r}_{1}^{2} \mathrm{~h}_{1}\right) \rho=\frac{3}{2} \mathrm{~m}
<br/> <br/>\end{aligned}
<br/> <br/>$$</div>


tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P1.db
title:
a-carbon-resistor-of-56-5-6-k-is-to-be-marked-with-rings-of-different-colours-for-its-identification-the-colour-code-sequence-will-be

slug:
a-carbon-resistor-of-56-5-6-k-is-to-be-marked-with-rings-of-different-colours-for-its-identification-the-colour-code-sequence-will-be-61849

question:
<div class="question">A carbon resistor of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>56</mn><mo>±</mo><mn>5</mn><mo>.</mo><mn>6</mn></mrow></mfenced><mo> </mo><mi>kΩ</mi></math> is to be marked with rings of different colours for its identification. The colour code sequence will be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">green, blue, orange, silver</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">blue, yellow, orange, silver</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">green, red, orange, silver</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">red, green, blue, gold</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">green, blue, orange, silver</span> </div>

answer:
<div class="solution"><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mfenced><mrow><mn>56</mn><mo>±</mo><mn>5</mn><mo>.</mo><mn>6</mn></mrow></mfenced><mo> </mo><mi>k</mi><mo> </mo><mi mathvariant="normal">Ω</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>56</mn><mo> </mo><mi mathvariant="normal">k</mi><mo> </mo><mi mathvariant="normal">Ω</mi><mo>±</mo><mn>10</mn><mo> </mo><mo>%</mo></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>56</mn><mo> </mo><mi mathvariant="normal">k</mi><mo> </mo><mi mathvariant="normal">Ω</mi></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>56</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>±</mo><mn>10</mn><mo> </mo><mo>%</mo><mo> </mo><mi mathvariant="normal">Ω</mi></math></p><p>As per the colour code for carbon resistors, the colour assigned to numbers</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>→</mo></math> Green<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>→</mo></math> Blue<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>→</mo></math> Orange</p><p>For <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mo>%</mo></math> accuracy or tolerance, the colour is silver. Hence, the bands of colours of carbon resistor in sequence are green, blue, orange and silver.</p></div>


tags: ['Physics', 'Thermodynamics', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P1.db
title:
a-carnots-heat-engine-works-between-the-temperatures-42-7-c-and-2-7-c-what-amount-of-heat-should-it-consume-per-second-to-deliver-mechanical-work-at-t

slug:
a-carnots-heat-engine-works-between-the-temperatures-42-7-c-and-2-7-c-what-amount-of-heat-should-it-consume-per-second-to-deliver-mechanical-work-at-t-90329

question:
<div class="question">A Carnot's heat engine works between the temperatures $427^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$. What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0 \mathrm{~kW} ?$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0.417 \mathrm{kcal} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4.17 \mathrm{kcal} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$41.7 \mathrm{kcal} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.212 \mathrm{kcal} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.417 \mathrm{kcal} / \mathrm{s}$</span> </div>

answer:
<div class="solution">The efficiency of the heat engine is
<br/> <br/>$$
<br/> <br/>\eta=1-\frac{T_{2}}{T_{1}}=1-\left(\frac{273+27 K}{273+427 K}\right)=\frac{4}{7}
<br/> <br/>$$
<br/> <br/>But $\quad \eta=\frac{\mathrm{W}}{\mathrm{Q}_{1}}$
<br/> <br/>$$
<br/> <br/>\therefore \mathrm{Q}_{1}=\frac{\mathrm{W}}{\eta}=\frac{1.0 \mathrm{~kW}}{4 / 7}=1.75 \mathrm{~kW}=0.417 \mathrm{kcal} / \mathrm{s}
<br/> <br/>$$
<br/> <br/>Thus, the engine would require 417 cal of heat per second, to deliver the requisite amount of work.</div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch1_P1.db
title:
a-certain-metal-sulphide-m-s-2-is-used-extensively-as-a-high-temperature-lubricant-if-ms-2-is-4006-by-mass-sulphur-metal-m-has-atomic-mass

slug:
a-certain-metal-sulphide-m-s-2-is-used-extensively-as-a-high-temperature-lubricant-if-ms-2-is-4006-by-mass-sulphur-metal-m-has-atomic-mass-31116

question:
<div class="question">A certain metal sulphide, $M S_2$, is used extensively as a high temperature lubricant. If $\mathrm{MS}_2$ is $40.06 \%$ by mass sulphur, metal $M$ has atomic mass.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$160 \mathrm{u}$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$64 \mathrm{u}$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$40 \mathrm{u}$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>$96 \mathrm{u}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$96 \mathrm{u}$</span> </div>

answer:
<div class="solution">$M S_2=M+32 \times 2=M+64$
<br/>$\%$ of sulphur $=\left(\frac{64}{M+64}\right) \times 100=40.06$
<br/>$M+64=\frac{6400}{40.06}$
<br/>$M+64=160$
<br/>$M=160-64=96$ u</div>


tags: ['Physics', 'Work Power Energy', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P1.db
title:
a-chain-of-mass-m-is-placed-on-a-smooth-table-with-1-n-of-its-length-l-hanging-over-the-edge-the-work-done-in-pulling-the-hanging-portion-of-the-chain

slug:
a-chain-of-mass-m-is-placed-on-a-smooth-table-with-1-n-of-its-length-l-hanging-over-the-edge-the-work-done-in-pulling-the-hanging-portion-of-the-chain-15139

question:
<div class="question">A chain of mass $\mathrm{M}$ is placed on a smooth table with $1 / \mathrm{n}$ of its length $\mathrm{L}$ hanging over the edge. The work done in pulling the hanging portion of the chain back to the surface of the table is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{MgL} / \mathrm{n}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{MgL} / 2 \mathrm{n}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{MgL} / \mathrm{n}^{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{MgL} / 2 \mathrm{n}^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{MgL} / 2 \mathrm{n}^{2}$</span> </div>

answer:
<div class="solution">$\quad \mathrm{W}=$ change in $\mathrm{PE}$ of $\mathrm{COM}$ of hanging part<br/>$$<br/>=\frac{\mathrm{M}}{\mathrm{n}} \mathrm{g} \frac{\mathrm{L}}{2 \mathrm{n}}=\frac{\mathrm{MgL}}{2 \mathrm{n}^{2}}<br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch1_P1.db
title:
a-charge-particle-is-moving-in-a-uniform-magnetic-field-2-i-3-j-t-if-it-has-an-acceleration-of-i-4-j-m-s-2-then-the-value-of-will-be-1

slug:
a-charge-particle-is-moving-in-a-uniform-magnetic-field-2-i-3-j-t-if-it-has-an-acceleration-of-i-4-j-m-s-2-then-the-value-of-will-be-1-30955

question:
<div class="question">A charge particle is moving in a uniform magnetic field $(2 \hat{i}+3 \hat{j}) \mathrm{T}$. If it has an acceleration of $(\alpha \hat{i}-4 \hat{j}) \mathrm{m} / \mathrm{s}^2$, then the value of $\alpha$ will be :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">6</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">12</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2</span> </li> </ul>

answer:
<div class="solution">Given that uniform magnetic field, $\vec{B}=(2 \hat{i}+3 \hat{j}) T$<br/>Acceleration $\vec{a}=(\alpha \hat{i}-4 \hat{j}) \mathrm{m} / \mathrm{s}^2$ We know that<br/>$F=q(\vec{v} \times \vec{B}) \Rightarrow m \vec{a}=q(\vec{v} \times \vec{B})$<br/>Here, $\vec{a} \perp \vec{B}$, so, $\vec{a} \cdot \vec{B}=0$<br/>$(\alpha \hat{i}-4 \hat{j})(2 \hat{i}+3 \hat{j})=0 \Rightarrow 2 \alpha-12=0 \Rightarrow \alpha=6$</div>


tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2011']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch1_P1.db
title:
a-charge-q-1-exerts-some-force-on-a-second-charge-q-2-if-a-3-rd-charge-q-3-is-brought-near-then-the-force-of-q-1-exerted-on-q-2

slug:
a-charge-q-1-exerts-some-force-on-a-second-charge-q-2-if-a-3-rd-charge-q-3-is-brought-near-then-the-force-of-q-1-exerted-on-q-2-79205

question:
<div class="question">A charge $\mathrm{Q}_{1}$ exerts some force on a second charge $\mathrm{Q}_{2}$. If a 3 rd charge $\mathrm{Q}_{3}$ is brought near, then the force of $\mathrm{Q}_{1}$ exerted on $\mathrm{Q}_{2}-$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">will increase</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">will decrease</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">will remain unchanged</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">will increase if $\mathrm{Q}_{3}$ is of the same sign as $\mathrm{Q}_{1}$ and will decrease if $\mathrm{Q}_{3}$ is of opposite sign.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">will remain unchanged</span> </div>


tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
a-charge-q-is-at-a-distance-l-2-above-a-square-of-side-l-then-what-is-the-flux-linked-with-the-surface-1

slug:
a-charge-q-is-at-a-distance-l-2-above-a-square-of-side-l-then-what-is-the-flux-linked-with-the-surface-1-30349

question:
<div class="question">A charge $+q$ is at a distance $L / 2$ above a square of side $\mathrm{L}$. Then what is the flux linked with the surface?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{q}}{4 \varepsilon_{0}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2 q}{3 \varepsilon_{0}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{q}}{6 \varepsilon_{0}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{6 \mathrm{q}}{\varepsilon_{0}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{q}}{6 \varepsilon_{0}}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/yVVO3LpdmZ20CqO6ICa0d7KACe8LFNfQG2cK4diHrEs.original.fullsize.png"/><br/>m{L}
<br/> <br/>The given square of side $L$ may be considered as one of the faces of a cube with edge $L$. Then given charge q will be considered to be placed at the centre of the cube. Then according to Gauss's theorem, the magnitude of the electric flux through the faces (six) of the cube is given by
<br/> <br/>$\phi=\mathrm{q} / \varepsilon_{0}$
<br/> <br/>Hence, electric flux through one face of the cube for the given square will be
<br/> <br/>$\phi^{\prime}=\frac{1}{6} \phi=\frac{\mathrm{q}}{6 \varepsilon_{0}}$</div>


tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch1_P1.db
title:
a-charge-q-is-at-a-distance-l-2-above-a-square-of-side-l-then-what-is-the-flux-linked-with-the-surface

slug:
a-charge-q-is-at-a-distance-l-2-above-a-square-of-side-l-then-what-is-the-flux-linked-with-the-surface-67625

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/DsLEBhteUM-6NOBx-ICwRFdm3sbtxNxlWNhELIGFTTQ.original.fullsize.png"/><br/><br/>The given square of side $\mathrm{L}$ may be considered as one of the faces of a cube with edge $\mathrm{L}$. Then given charge $\mathrm{q}$ will be considered to be placed at the centre of the cube. Then according to Gauss's theorem, the magnitude of the electric flux through the faces (six) of the cube is given by<br/>$$<br/>\phi=\mathrm{q} / \varepsilon_{0}<br/>$$<br/>Hence, electric flux through one face of the cube for the given square will be<br/>$\phi^{\prime}=\frac{1}{6} \phi=\frac{\mathrm{q}}{6 \varepsilon_{0}}$</div>


tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P1.db
title:
a-charge-q-is-placed-at-each-of-the-opposite-corners-of-a-square-a-charge-q-is-placed-at-each-of-the-other-two-corners-if-the-net-electrical-force-on--1

slug:
a-charge-q-is-placed-at-each-of-the-opposite-corners-of-a-square-a-charge-q-is-placed-at-each-of-the-other-two-corners-if-the-net-electrical-force-on-1-89497

question:
<div class="question">A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $\frac{Q}{q}$ equals:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-1$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-\frac{1}{\sqrt{2}}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$-2 \sqrt{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-2 \sqrt{2}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Hts9_DP0I9bJeoH6q8wbY_mrR2-h2VwGI2mzTegRaJc.original.fullsize.png"/><br/> <br/> <br/>It is given that $\vec{F}_{A}+\vec{F}_{B}+\vec{F}_{D}=0$
<br/> <br/>Where $\vec{F}_{A}, \vec{F}_{B}$ and $\vec{F}_{D}$ are the forces applied by charges placed at $A, B$ and $D$ on the charge placed at $C$.
<br/> <br/>$\begin{array}{l}
<br/> <br/>\Rightarrow \overrightarrow{\mathrm{F}}_{\mathrm{B}}+\overrightarrow{\mathrm{F}}_{\mathrm{D}}=-\overrightarrow{\mathrm{F}}_{\mathrm{A}} \\
<br/> <br/>\left|\overrightarrow{\mathrm{F}}_{\mathrm{B}}+\overrightarrow{\mathrm{F}}_{\mathrm{D}}\right|=\sqrt{2} \frac{\mathrm{KqQ}}{\mathrm{a}^{2}} \\
<br/> <br/>\Rightarrow\left|\overrightarrow{\mathrm{F}}_{\mathrm{A}}\right|=\frac{\mathrm{KQ}^{2}}{2 a^{2}} \\
<br/> <br/>\therefore \sqrt{2} \frac{\mathrm{KqQ}}{a^{2}}=-\frac{\mathrm{KQ}^{2}}{2 a^{2}} \\
<br/> <br/>\Rightarrow \frac{\mathrm{Q}}{q}=-2 \sqrt{2}
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Capacitance', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P1.db
title:
a-charged-capacitor-of-capacitance-c-is-discharging-through-a-resistor-of-resistance-r-at-what-time-the-charge-on-the-capacitor-is-equal-to-one-half-o

slug:
a-charged-capacitor-of-capacitance-c-is-discharging-through-a-resistor-of-resistance-r-at-what-time-the-charge-on-the-capacitor-is-equal-to-one-half-o-68582

question:
<div class="question">A charged capacitor of capacitance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> is discharging through a resistor of resistance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math>. At what time the charge on the capacitor is equal to one half of its initial value?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>R</mi><mi>C</mi></mrow><mn>2</mn></mfrac></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>R</mi><mi>C</mi></mrow><mrow><msub><mi>log</mi><mi>e</mi></msub><mn>2</mn></mrow></mfrac></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>C</mi><msub><mi>log</mi><mrow><mi>e</mi><mo> </mo></mrow></msub><mn>2</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mi>R</mi><mi>C</mi></mrow></mfrac><msub><mi>log</mi><mi>e</mi></msub><mn>2</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>C</mi><msub><mi>log</mi><mrow><mi>e</mi><mo> </mo></mrow></msub><mn>2</mn></math></span> </div>

answer:
<div class="solution"><p>The charge on the capacitor at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> in a discharging circuit is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msub><mi>q</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi><mo>/</mo><mi>τ</mi></mrow></msup></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi><mo>=</mo><mi>R</mi><mi>C</mi><mo>=</mo></math> time constant<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math>               <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msub><mi>q</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi><mo>/</mo><mi>R</mi><mi>C</mi></mrow></msup></math></p><p>when, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>  </mo><mi>q</mi><mo>=</mo><mfrac><msub><mi>q</mi><mn>0</mn></msub><mn>2</mn></mfrac></math></p><p>then  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>q</mi><mn>0</mn></msub><mn>2</mn></mfrac><mo>=</mo><msub><mi>q</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi><mo>/</mo><mi>R</mi><mi>C</mi></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi><mo>/</mo><mi>R</mi><mi>C</mi></mrow></msup></math></p><p>Taking natural log on both side <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mi>e</mi></msub><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mo>=</mo><msub><mi>log</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi><mo>/</mo><mi>R</mi><mi>C</mi></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msub><mi>log</mi><mi>e</mi></msub><mn>2</mn><mo>=</mo><mo>-</mo><mfrac><mi>t</mi><mrow><mi>R</mi><mi>C</mi></mrow></mfrac><msub><mi>log</mi><mi>e</mi></msub><mi>e</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>t</mi><mo>=</mo><mi>R</mi><mi>C</mi><msub><mi>log</mi><mi>e</mi></msub><mn>2</mn></math></p></div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2015']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$2 \%$</span> </div>
source_db: MarksBatch1_P1.db
title:
a-charged-particle-moving-in-a-uniform-magnetic-field-and-losses-4-of-its-kinetic-energy-the-radius-of-curvature-of-its-path-changes-by

slug:
a-charged-particle-moving-in-a-uniform-magnetic-field-and-losses-4-of-its-kinetic-energy-the-radius-of-curvature-of-its-path-changes-by-88457

question:
<div class="question">A charged particle moving in a uniform magnetic field and losses $4 \%$ of its kinetic energy. The radius of curvature of its path changes by</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$2 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4 \%$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10 \%$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$12 \%$</span> </li> </ul>

answer:
<div class="solution">As we know $\mathrm{F}=\mathrm{qvB}=\frac{\mathrm{mv}^{2}}{\mathrm{r}}$
<br/> <br/>$\therefore \mathrm{r}=\frac{\mathrm{mv}}{\mathrm{Bq}}$
<br/> <br/>And $\mathrm{KE}=\mathrm{k}=\frac{1}{2} \mathrm{mv}^{2}$
<br/> <br/>$\therefore \mathrm{mv}=\sqrt{2 \mathrm{~km}}$
<br/> <br/>$\therefore \mathrm{r}=\frac{\mathrm{mv}}{\mathrm{qB}}=\frac{\sqrt{2 \mathrm{~km}}}{\mathrm{qB}}$
<br/> <br/>$\Rightarrow r \propto \sqrt{k}$ or $r=c^{1 / 2}(c$ is a constant $)$ $\frac{\mathrm{dr}}{\mathrm{dr}}=\mathrm{c} \frac{\mathrm{dk}^{1 / 2}}{\mathrm{dr}}$ or $\frac{\mathrm{c} \Delta \mathrm{k}}{\Delta \mathrm{r}}=2 \sqrt{\mathrm{k}}$
<br/> <br/>$\frac{\Delta r}{r}=\frac{\mathrm{c} \Delta \mathrm{k}}{2 \sqrt{\mathrm{k}} \mathrm{c} \sqrt{\mathrm{k}}}=\frac{\Delta \mathrm{k}}{2 \mathrm{k}}$
<br/> <br/>Therefore percentage changes in radius of path,
<br/> <br/>$\frac{\Delta r}{r} \times 100=\frac{\Delta k}{2 k} \times 100=2 \%$</div>


tags: ['Physics', 'Rotational Motion', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P1.db
title:
a-circular-disc-of-radius-r-and-thickness-6-r-has-moment-inertia-i-about-an-axis-passing-through-its-centre-perpendicular-to-its-plane-it-is-melted-an

slug:
a-circular-disc-of-radius-r-and-thickness-6-r-has-moment-inertia-i-about-an-axis-passing-through-its-centre-perpendicular-to-its-plane-it-is-melted-an-42534

question:
<div class="question">A circular disc of radius $\mathrm{R}$ and thickness $\frac{R}{6}$ has moment inertia I about an axis passing through its centre perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$I$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2 I}{8}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{I}{5}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{I}{10}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{I}{5}$</span> </div>

answer:
<div class="solution">According to problem disc is melted and recasted into a solid sphere so their volume
<br/> <br/>$$
<br/> <br/>\begin{array}{c}
<br/> <br/>\text { will be same. } \\
<br/> <br/>V_{\text {Disc }}=V_{\text {Sphere }} \Rightarrow \pi R_{\text {Disc }}^{2} t=\frac{4}{3} \pi R_{\text {Sphere }}^{3} \\
<br/> <br/>\Rightarrow \pi R_{\text {Disc }}^{2}\left(\frac{R_{\text {Disc }}}{6}\right)=\frac{4}{3} \pi R_{\text {Sphere }}^{3}\left[t=\frac{R_{\text {Disc }}}{6}, \text { given }\right] \\
<br/> <br/>\Rightarrow R_{\text {Disc }}^{3}=8 R_{\text {Sphere }}^{3} \Rightarrow R_{\text {Sphere }}=\frac{R_{\text {Disc }}}{2}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Moment of inertia of disc
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>I_{\text {Disc }}=\frac{1}{2} M R_{\text {Disc }}^{2}=I \text { (given) } \\
<br/> <br/>\therefore \text { M }\left(R_{\text {Disc }}\right)^{2}=2 I
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Moment of inertia of sphere
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>I_{\text {Sphere }}=\frac{1}{2} M R_{\text {Sphere }}^{2} \\
<br/> <br/>=\frac{2}{5} M\left(\frac{R_{\text {Disc }}}{2}\right)^{2}=\frac{M}{10}\left(R_{\text {Disc }}\right)^{2}=\frac{2 I}{10}=\frac{I}{5}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Mathematics', 'Sets and Relations', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">60</span> </div>
source_db: MarksBatch1_P1.db
title:
a-class-has-175-students-the-following-data-shows-the-number-of-students-obtaining-one-or-more-subjects-mathematics-100-physics-70-chemistry-40-mathem-1

slug:
a-class-has-175-students-the-following-data-shows-the-number-of-students-obtaining-one-or-more-subjects-mathematics-100-physics-70-chemistry-40-mathem-1-46130

question:
<div class="question">A class has 175 students. The following data shows the number of students obtaining one or more subjects. Mathematics 100 , Physics 70 , Chemistry 40; Mathematics and Physics 30 , Mathematics and Chemistry 28 , Physics and Chemistry 23; Mathematics, Physics and Chemistry $18 .$ How many students have offered Mathematics alone?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">35</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">48</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">60</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">22</span> </li> </ul>

answer:
<div class="solution">$\begin{aligned} &amp; n(\mathrm{M} \text { alone }) \\ &amp;=n(\mathrm{M})-n(\mathrm{M} \cap \mathrm{C})-n(\mathrm{M} \cap \mathrm{P})+n(\mathrm{M} \cap \mathrm{C} \cap \mathrm{P}) \\ &amp;=100-28-30+18=60 \end{aligned}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/4cmZ9HmBbcB8qSB0F-frwWesAJkLfXEnrdlHo_3SXNQ.original.fullsize.png"/></div>


tags: ['Mathematics', 'Sets and Relations', 'BITSAT', 'BITSAT 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">60</span> </div>
source_db: MarksBatch1_P1.db
title:
a-class-has-175-students-the-following-data-shows-the-number-of-students-obtaining-one-or-more-subjects-mathematics-100-physics-70-chemistry-40-mathem

slug:
a-class-has-175-students-the-following-data-shows-the-number-of-students-obtaining-one-or-more-subjects-mathematics-100-physics-70-chemistry-40-mathem-89163


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P1.db
title:
a-coil-10-turns-and-a-resistance-of-20-is-connected-in-series-with-bg-of-resistance-30-the-coil-is-placed-with-its-plane-perpendicular-to-the-directio

slug:
a-coil-10-turns-and-a-resistance-of-20-is-connected-in-series-with-bg-of-resistance-30-the-coil-is-placed-with-its-plane-perpendicular-to-the-directio-81666

question:
<div class="question">A coil 10 turns and a resistance of $20 \Omega$ is connected in series with B.G of resistance $30 \Omega$. The coil is placed with its plane perpendicular to the direction of a uniform magnetic field of induction $10^{-2} \mathrm{~T}$. If it is now turned through an angle of $60^{\circ}$ about an axis in its plane. Find the charge induced in the coil. (Area of a coil $=10^{-2} \mathrm{~m}^{2}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \times 10^{-5} \mathrm{C}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3.2 \times 10^{-5} \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1 \times 10^{-5} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5.5 \times 10^{-5} \mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 \times 10^{-5} \mathrm{C}$</span> </div>

answer:
<div class="solution">Given: $\mathrm{n}=10$ turns, $\mathrm{R}_{\text {coil }}=20 \Omega, \mathrm{R}_{\mathrm{G}}=30 \Omega$, Total resistance in the circuit $=20+30$
<br/> <br/>$=50 \Omega$
<br/> <br/>$\mathrm{A}=10^{-2} \mathrm{~m}^{2}, \mathrm{~B}=10^{-2} \mathrm{~T}, \phi_{1}=0^{\circ}, \phi_{2}=60^{\circ}$
<br/> <br/>$\mathrm{q}=\frac{\phi_{1}-\phi_{2}}{\mathrm{R}}=\frac{\mathrm{Bn} \mathrm{A} \cos \theta_{1}-\mathrm{Bn} \mathrm{A} \cos \theta_{2}}{\mathrm{R}}$
<br/> <br/>$=\frac{\operatorname{Bn} \mathrm{A}(\cos 0-\cos 60)}{\mathrm{R}}=\frac{\mathrm{BnA}(1-0.5)}{\mathrm{R}}$
<br/> <br/>$=\frac{0.5 \times 10^{-2} \times 10 \times 10^{-2}}{50}=\frac{50 \times 10^{-5}}{50}$
<br/> <br/>$=1 \times 10^{-5} \mathrm{C} \quad$ (Charge induced in a coil)</div>


tags: ['Physics', 'Alternating Current', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P1.db
title:
a-coil-has-resistance-30-ohm-and-inductive-reactance-20-ohm-at-50-hz-frequency-if-an-ac-source-of-200-volt-100-hz-is-connected-across-the-coil-the-cur

slug:
a-coil-has-resistance-30-ohm-and-inductive-reactance-20-ohm-at-50-hz-frequency-if-an-ac-source-of-200-volt-100-hz-is-connected-across-the-coil-the-cur-36594

question:
<div class="question">A coil has resistance 30 ohm and inductive reactance 20 ohm at $50 \mathrm{~Hz}$ frequency. If an ac source, of 200 volt, $100 \mathrm{~Hz},$ is connected across the coil, the current in the coil will be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$4.0 \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$8.0 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$7.2 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2.0 \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4.0 \mathrm{~A}$</span> </div>

answer:
<div class="solution">If $\omega=50 \times 2 \pi$ then $\omega \mathrm{L}=20 \Omega$ If $\omega^{\prime}=100 \times 2 \pi$ then $\omega^{\prime} \mathrm{L}=40 \Omega$<br/>Current flowing in the coil is<br/>$$<br/>\mathrm{I}=\frac{200}{\mathrm{Z}}=\frac{200}{\sqrt{\mathrm{R}^{2}+\left(\omega^{\prime} \mathrm{L}\right)^{2}}}=4 \mathrm{~A}<br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
title:
a-coil-in-the-shape-of-an-equilateral-triangle-of-side-l-is-suspended-between-the-pole-pieces-of-a-permanent-magnet-such-that-b-is-in-plane-of-the-coi

slug:
a-coil-in-the-shape-of-an-equilateral-triangle-of-side-l-is-suspended-between-the-pole-pieces-of-a-permanent-magnet-such-that-b-is-in-plane-of-the-coi-10741

question:
<div class="question">A coil in the shape of an equilateral triangle of side <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> is suspended between the pole pieces of a permanent magnet such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> is in plane of the coil. If due to a current <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math> in the triangle, a torque <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi></math> rests on it, the side <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> of the triangle is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mfenced><mfrac><mi>τ</mi><mrow><msqrt><mn>3</mn></msqrt><mi>B</mi><mi>i</mi></mrow></mfrac></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><msqrt><mn>3</mn></msqrt></mfrac><mfenced><mfrac><mi>τ</mi><mrow><mi>B</mi><mi>i</mi></mrow></mfrac></mfenced></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><span style="color:null;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mfenced><mfrac><mi>τ</mi><mrow><mi>B</mi><mi>i</mi></mrow></mfrac></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></math></span></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msqrt><mn>3</mn></msqrt></mfrac><mfenced><mfrac><mi>τ</mi><mrow><mi>B</mi><mi>i</mi></mrow></mfrac></mfenced></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mfenced><mfrac><mi>τ</mi><mrow><msqrt><mn>3</mn></msqrt><mi>B</mi><mi>i</mi></mrow></mfrac></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></math></span> </div>

answer:
<div class="solution"><p>Torque acting on equilateral triangle in a magnetic field <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> is</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi><mo>=</mo><mi>i</mi><mo> </mo><mi>A</mi><mi>B</mi><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/37d03392-518a-49a8-9339-d8c73454232d-image.png" style="width: 260px; height: 248px;"/></p><p>Area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LMN</mi></math>,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac><msup><mi>l</mi><mn>2</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>90</mn><mo>°</mo></math></p><p>Substituting the given values in expression for torque, we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi><mo>=</mo><mi>i</mi><mo>×</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>4</mn></mfrac><mo> </mo><msup><mi>l</mi><mn>2</mn></msup><mo> </mo><mi>B</mi><mo> </mo><mi>sin</mi><mo> </mo><mn>90</mn><mo>°</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>4</mn></mfrac><mi>i</mi><msup><mi>l</mi><mn>2</mn></msup><mi>B</mi></math>    <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>∵</mo><mo> </mo><mo> </mo><mi>sin</mi><mo> </mo><mn>90</mn><mo>°</mo><mo>=</mo><mn>1</mn></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>l</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>4</mn><mi>τ</mi></mrow><mrow><msqrt><mn>3</mn></msqrt><mo> </mo><mi>B</mi><mi>i</mi></mrow></mfrac></math></p><p>Here, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>2</mn><mo> </mo><msup><mfenced><mfrac><mi>τ</mi><mrow><msqrt><mn>3</mn></msqrt><mo> </mo><mi>B</mi><mi>i</mi></mrow></mfrac></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></math></p></div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P1.db
title:
a-coin-is-tossed-7-times-each-time-a-man-calls-head-find-the-probability-that-he-wins-the-toss-on-more-occasions

slug:
a-coin-is-tossed-7-times-each-time-a-man-calls-head-find-the-probability-that-he-wins-the-toss-on-more-occasions-56725

question:
<div class="question">A coin is tossed 7 times. Each time a man calls head. Find the probability that he wins the toss on more occasions.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{2}{3}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{1}{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{2}$</span> </div>

answer:
<div class="solution">The man has to win at least 4 times.
<br/> <br/>$$
<br/> <br/>\begin{array}{r}
<br/> <br/>\therefore \text { Reqd. probability }= \\
<br/> <br/>\qquad \begin{array}{r}
<br/> <br/>7 \mathrm{C}_{4}\left(\frac{1}{2}\right)^{4} \cdot\left(\frac{1}{2}\right)^{3}+{ }^{7} \mathrm{C}_{5}\left(\frac{1}{2}\right)^{5} \cdot\left(\frac{1}{2}\right)^{2} \\
<br/> <br/>+{ }^{7} \mathrm{C}_{6}\left(\frac{1}{2}\right)^{6} \cdot \frac{1}{2}+{ }^{7} \mathrm{C}_{7}\left(\frac{1}{2}\right)^{7} \\
<br/> <br/>=\left({ }^{7} \mathrm{C}_{4}+{ }^{7} \mathrm{C}_{5}+{ }^{7} \mathrm{C}_{6}+{ }^{7} \mathrm{C}_{7}\right) \cdot \frac{1}{2^{7}}=\frac{64}{2^{7}}=\frac{1}{2}
<br/> <br/>\end{array}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
title:
a-coin-is-tossed-7-times-each-time-a-man-calls-head-the-probability-that-he-wins-the-toss-at-least-four-times-is

slug:
a-coin-is-tossed-7-times-each-time-a-man-calls-head-the-probability-that-he-wins-the-toss-at-least-four-times-is-10098

question:
<div class="question">A coin is tossed <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math> times. Each time a man calls head. The probability that he wins the toss at least four times is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>4</mn></mfrac></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>8</mn></mfrac></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>6</mn></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></span> </div>

answer:
<div class="solution"><p>The man has to win atleast <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> times.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Required probability</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mmultiscripts><mi>C</mi><mn>4</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>4</mn></msup><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>3</mn></msup><mo>+</mo><mmultiscripts><mi>C</mi><mn>5</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>5</mn></msup><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mo>+</mo><mmultiscripts><mi>C</mi><mn>6</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>6</mn></msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mo>+</mo><mmultiscripts><mi>C</mi><mn>7</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>7</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfenced><mrow><mmultiscripts><mi>C</mi><mn>4</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi>C</mi><mn>5</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi>C</mi><mn>6</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi>C</mi><mn>7</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts></mrow></mfenced><mo>×</mo><mfrac><mn>1</mn><msup><mn>2</mn><mn>7</mn></msup></mfrac><mo>=</mo><mfrac><mn>64</mn><msup><mn>2</mn><mn>7</mn></msup></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></p></div>


tags: ['Physics', 'Semiconductors', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
title:
a-common-emitter-amplifier-has-a-voltage-gain-of-50-an-input-impedance-of-100-and-an-output-impedance-of-200-the-power-gain-of-the-amplifier-is-4

slug:
a-common-emitter-amplifier-has-a-voltage-gain-of-50-an-input-impedance-of-100-and-an-output-impedance-of-200-the-power-gain-of-the-amplifier-is-4-47559

question:
<div class="question">A common emitter amplifier has a voltage gain of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math>, an input impedance of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math> and an output impedance of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math>. The power gain of the amplifier is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1250</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1250</mn></math></span> </div>

answer:
<div class="solution"><p>Voltage gain <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi mathvariant="normal">β</mi><mo>×</mo></math> impedance gain</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mn>50</mn><mo>=</mo><mi mathvariant="normal">β</mi><mo>×</mo><mfrac><mn>200</mn><mn>100</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi mathvariant="normal">β</mi><mo>=</mo><mn>25</mn></math></p><p>Also power gain <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mi mathvariant="normal">β</mi><mn>2</mn></msup><mo>×</mo></math> impedance gain </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mfenced><mn>25</mn></mfenced><mn>2</mn></msup><mo>×</mo><mfrac><mn>200</mn><mn>100</mn></mfrac><mo>=</mo><mn>1250</mn></math></p></div>


title: a-compound-of-xe-and-f-is-found-to-have-535-of-xe-what-is-oxidation-number-of-xe-in-this-compound
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch1_P1.db
slug:
a-compound-of-xe-and-f-is-found-to-have-535-of-xe-what-is-oxidation-number-of-xe-in-this-compound-48924

question:
<div class="question">A compound of Xe and $\mathrm{F}$ is found to have $53.5 \%$ of Xe. What is oxidation number of Xe in this compound?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">-4</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">4</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">6</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">$\mathrm{Xe}=53.5 \% \therefore \mathrm{F}=46.5 \%$
<br/> <br/>Relative number of atoms Xe
<br/> <br/>$$
<br/> <br/>=\frac{53.5}{131.2}=0.4 \text { and } \mathrm{F}=\frac{46.5}{19}=2.4
<br/> <br/>$$
<br/> <br/>Simple ratio $\mathrm{Xe}=1$ and $\mathrm{F}=6 ;$ Molecular formula is $\mathrm{XeF}_{6}$
<br/> <br/>O. $\mathrm{N}$.of $\mathrm{Xe}$ is +6</div>


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
title:
a-conducting-circular-loop-is-placed-in-a-uniform-magnetic-field-b-0-025-t-with-its-plane-perpendicular-to-the-loop-the-radius-of-the-loop-is-made-to-

slug:
a-conducting-circular-loop-is-placed-in-a-uniform-magnetic-field-b-0-025-t-with-its-plane-perpendicular-to-the-loop-the-radius-of-the-loop-is-made-to-66110

question:
<div class="question">A conducting circular loop is placed in a uniform magnetic field, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>025</mn><mo> </mo><mi mathvariant="normal">T</mi></math> with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi>mm</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>. The induced emf when the radius is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>cm</mi></math>, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>π</mi><mo> </mo><mi>μV</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi><mo> </mo><mi>μV</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac><mi>μV</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>μV</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi><mo> </mo><mi>μV</mi></math></span> </div>

answer:
<div class="solution"><p>Here, magnetic field,<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>025</mn><mo> </mo><mi mathvariant="normal">T</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Magnetic flux <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi><mo>=</mo><mi>B</mi><mo>·</mo><mi>A</mi><mo>=</mo><mi>B</mi><mo>·</mo><mi>π</mi><msup><mi>r</mi><mn>2</mn></msup></math></p><p>Induced <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emf</mi><mo> </mo><mfenced close="|" open="|"><mi mathvariant="normal">e</mi></mfenced><mo>=</mo><mfrac><mrow><mi>d</mi><mi>ϕ</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>B</mi><mi>π</mi><mn>2</mn><mi>r</mi><mo>·</mo><mfrac><mrow><mi>d</mi><mi>r</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>025</mn><mo>×</mo><mi>π</mi><mo>×</mo><mn>2</mn><mo>×</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>×</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>π</mi><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn><mo> </mo></mrow></msup><mo> </mo><mi mathvariant="normal">V</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>π</mi><mo> </mo><mi>μV</mi></math></p></div>


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P1.db
title:
a-conducting-circular-loop-is-placed-in-a-uniform-magnetic-field-of-004-t-with-its-plane-perpendicular-to-the-magnetic-field-the-radius-of-the-loop-st

slug:
a-conducting-circular-loop-is-placed-in-a-uniform-magnetic-field-of-004-t-with-its-plane-perpendicular-to-the-magnetic-field-the-radius-of-the-loop-st-65182

question:
<div class="question">A conducting circular loop is placed in a uniform magnetic field of $0.04 \mathrm{~T}$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2 \mathrm{~mm} / \mathrm{s}$. The induced emf in the loop when the radius is $2 \mathrm{~cm}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4.8 \pi \mu \mathrm{V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.8 \pi \mu \mathrm{V}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.6 \pi \mu \mathrm{V}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$3.2 \pi \mu \mathrm{V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3.2 \pi \mu \mathrm{V}$</span> </div>

answer:
<div class="solution">Induced emf in the loop is given by
<br/> <br/>$\mathrm{e}=-\mathrm{B} \cdot \frac{\mathrm{d} \mathrm{A}}{\mathrm{dt}}$ where $\mathrm{A}$ is the area of the loop.
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\mathrm{e}=-\mathrm{B} \cdot \frac{\mathrm{d}}{\mathrm{dt}}\left(\pi \mathrm{r}^{2}\right)=-\mathrm{B} \pi 2 \mathrm{r} \frac{\mathrm{dr}}{\mathrm{dt}} \\
<br/> <br/>\mathrm{r}=2 \mathrm{~cm}=2 \times 10^{-2} \mathrm{~m} \\
<br/> <br/>\mathrm{dr}=2 \mathrm{~mm}=2 \times 10^{-3} \mathrm{~m} \\
<br/> <br/>\mathrm{dt}=1 \mathrm{~s} \\
<br/> <br/>\mathrm{e}=-0.04 \times 3.14 \times 2 \times 2 \times 10^{-2} \times \frac{2 \times 10^{-3}}{1} \mathrm{~V} \\
<br/> <br/>=0.32 \pi \times 10^{-5} \mathrm{~V} \\
<br/> <br/>=3.2 \pi \times 10^{-6} \mathrm{~V} \\
<br/> <br/>=3.2 \pi \mu \mathrm{V}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
source_db: MarksBatch1_P1.db
title:
a-conducting-circular-loop-of-radius-r-carries-a-constant-current-i-it-is-placed-in-a-uniform-magnetic-field-b-0-such-that-b-0-is-perpendicular-to-the

slug:
a-conducting-circular-loop-of-radius-r-carries-a-constant-current-i-it-is-placed-in-a-uniform-magnetic-field-b-0-such-that-b-0-is-perpendicular-to-the-18209

question:
<div class="question">A conducting circular loop of radius $r$ carries a constant current $i .$ It is placed in a uniform magnetic field $\overrightarrow{\mathrm{B}}_{0}$ such that $\overrightarrow{\mathrm{B}}_{0}$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$i r \mathrm{~B}_{0}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \pi i r \mathrm{~B}_{0}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\pi$ ir $\mathrm{B}_{0}$</span> </li> </ul>

answer:
<div class="solution">The magnetic field is perpendicular to the plane of the paper. Let us consider two diametrically opposite elements. By Fleming's Left hand rule on element $\mathrm{AB}$ the direction of force will be Leftwards and the magnitude will be<br/>$$<br/>\mathrm{dF}=\operatorname{Idl} \mathrm{B} \sin 90^{\circ}=\mathrm{IdIB}<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/XBTY49ILQHjW94fWn2TJCWNCt3sba5dlj7-xHNKczf4.original.fullsize.png"/></div>


